While I was developing software that can deal with very large numbers, I met with a question and the question was can we actually get a result value from calculating true infinity numbers. It took me sometimes to analyze infinity numbers through programming by producing code and script that can calculate very large numbers.

After analyzing the properties of infinity numbers, I came to a conclusion. From the conclusion, I define that it is possible to calculate a mathematical equation’s result value for any infinity numbers. For some instance, we may never be able to get the result value for the entire equation because the numbers are infinite in length. Nevertheless, we can still produce part of the result value. In other instance, it is possible to actually get a result value that would be very similar to the actual result value of an entire equation of infinity numbers. From my conclusion, I compare infinity to time and from there I wrote the infinity formula.

### Infinity – The Formula

#### Is An Infinity Number A Number?

When we first talk about an infinity number, the first question would come up to mind is can we classify a number that is infinitely in length as a number? In my opinion, whether if the number is infinitely in length or not, we can always classify the number as a number. The closest evidence that I came up with to back up this theory is time. I would use time for a comparison in this case.

As when we are looking at time as the subject, time is also infinitely in measurement. No one would know if time would flow infinitely or will time meet a wall and will end. For the property of time, we know that we can see events that occurred in the past but not the present nor the future. We may be able to predict the future bases on statistical data but would not be able to see events that will occur in the future.

Also, we, ourselves can never see events that are occurring in the present. The events of now that is occurring right in front of our eyes seem like the present, and our brain perceives it that way. Nevertheless, what we are seeing in our eyes are actually the past. It would take sometimes for light to hit an object and then reflect off the object into our eyes. When our eyes receiving the light, our brain would have to process the lights into images. Because of the speed of light and because of how fast our brain process data, the process of translating an event that occurs in front of our eyes into an image would be really fast and would be completed in less than a microsecond or a nanosecond. The fast speed of the process would let our brain perceive the event that occurred in front of us as if we are actually seeing the present. However, that event actually occurred less than a nanosecond in the past. In my opinion, in a true equation, whether if the event occurred one year ago or one nanosecond ago it would still be considered as an event of the past and not the present.

When we take this to a micro scale, even if we are standing in front of a mirror and looking at ourselves, the images that we are seeing in the mirror are still the images of the past and not the images of the present. On a larger scale, if we are looking at a planet that is one billion light year distance away from us, we are not seeing that planet present. We are actually seeing the past of that planet. It would take one billion years for light to travel from that planet to our planet, Thus, if that planet was destroyed or turned into a planet that habitable by life forms half a billion years ago, we would not know until half a billion years later. This same principle also applies to our closest star, which would be the Sun. If there are any changes on the surface of the Sun, we would not be able to detect the changes until at least eight minutes later.

Not just our eyes that can’t see events that occurred in the present, the pain that we feel or the feeling of touching an object are also events that occurred in the past. When an object touched our body, it would take a very small amount of time for our nerve to be able to send a signal to our brain, and with that signal from the nerve, our brain would be able to process the signal into what we can describe as feelings.

Even when we are playing games on the computer or typing something on the computer. To us, it almost seems like when we are typing something on the computer, the words would be displayed so quickly that it is actually the present. Nevertheless, we, in fact, pressed the key on the keyboard some microseconds or nanoseconds ago.

Is there a method for us to be able to perceive events of the present? In my opinion, at the current state, I do not believe that we can perceive events that occur at their exact moments. Nevertheless, I do believe that to be able to perceive events that occur right at the exact moments of when they occurred is to be able to move forward in time and look back at the events. Only then, we would be able to perceive events that occur at their exact moment. In short, to be able to see the present is to be able to see the future and look back in time. Will technology or will our body develop to give us the ability to perceive events of the present by looking forward into the future? I would never know.

When comparing time to an infinity number, I would treat time as a mathematical equation. What events that we have seen that already occurred in the past would be similar to seeing numbers that we had already seen and might have applied a calculation to. Thus, when we are asking the question if an infinity number is a number would be similar to asking if the infinity time is time. Time is infinite in the amount and in my opinion, whether if the events in time have happened yet or not, they would still be considered as time. Therefore in principle, if we were to receive an infinite string of digits, the digits that we have seen are numbers and the digits that we haven’t seen are still numbers. In my opinion, it just because the numbers are infinitely in length does not mean that they are not a number. They are still numbers, just that they are numbers that are infinitely in length.

For an example, my birthday that happened last year would be considered as an event of time that had already occurred. My birthday of the future or how many birthdays would I have left would still be considered as events of time. These time events, however, have not occurred but are time events of the future. If my birthday of the future does not happen, another event of time would replace the time event of what suppose to be my birthday. Nevertheless, these events would still be considered as an event that occurs in time or an event of time.

In my conclusion, I concluded that a number, whether infinitely in length or not should still be considered as a number. Therefore, an infinity number is still a number, it just that the infinity number is infinitely in length.

#### Infinity Numbers Are Same In Length

When looking at the length of infinity numbers, I asked myself, can one infinity number be longer than another infinity numbers in terms of the amount of digit one number can have? With some analysis, in my opinion, infinity numbers are always the same length. I drew my conclusion bases on one simple principle, and that principle is if the numbers are infinitely in length that means there is no limit on the amount of digits one number can have, and that also means, any number that is infinitely in length will never have an ending. In another explanation, if we are using the term infinity for a length then infinity is the largest available length in any type of measurement. This is because infinity will never end, and due to that, there would not be another unit of measurement that is larger than infinity as a unit of measurement. Since infinity as a length is the largest available length, there would not be another length that is larger than the infinity length. There will be other lengths that are smaller than the infinity length, nevertheless, infinity length can neither be smaller than itself. With that perspective in mind, the infinity length can’t be larger or smaller than itself.

To put the perspective above in context, I will demonstrate some examples. For the first example, we have two numbers and each number contained 1 trillion digits. If we were to discuss in regard to the length property of those numbers, then we know that they are both 1 trillion digits in length, and if we were to ask which number is the longer or the shorter number, then we know that both numbers are the same in length. The reason of why the numbers are the same in length is because both numbers are 1 trillion digits long. Now, if one number is 1 trillion digits long and the other number is 1 trillion and 1 digits long, then the numbers are now different in length. Thus, in this instance, if we were to measure the length of the numbers, the longer number would be the number that has 1 trillion and 1 digits. It may seem that the length of 1 trillion digits is a superbly huge length, nevertheless, the 1 trillion digits length is not endless and is calculable. When this principle is applied to infinity lengths, the property would be similar. If both numbers can never run out of digits then either number can’t be the larger number bases on their length. Also, either number can’t be the shorter number bases on how many digits one number had.

For another more complicated example, I will use a real life example. In this example, we have two cars, one is black and one is white. The white car will travel a route that is 1000km long, and the black car will travel another route that is 1000km long. Both cars will be driven at the same speed. The white car started its route 5 hours before the black car. Now, if we were to ask which car finish their route first then it is obvious that the white car will. Nevertheless, if we were to ask which car will travel the longer or the shorter distances then we know that the answer is both cars will travel the same distance. This is because they will both travel a route that is 1000km long. Now, if the white car was to route through an additional route that is just 1km long, then it is obvious that the white car will travel the longer distance. Nevertheless, when coming back to the 1000km route, 1000km can’t be smaller or larger than 1000km. This is because 1000km is the same length as 1000km. If we were to use a distance of infinity instead of using the distance of 1000km, then both car will still, in fact, travel the same distances.

For the final example, let imagine that we have two pieces of paper that are so large that they are infinitely in size. If we were to write down one random digit onto each piece of paper at the same time and at the rate of one digit per second for an infinite amount of second, at any moment during the process, both of our pieces of paper will always have the same amount of digits, and the amount of digits that each piece of paper is going to have is going to be endless.

When it comes to a fractional part value for infinity numbers, the same in length property would also attach to the numbers. If we are going to say that there is an infinite amount of digit before and after the decimal for both numbers. That means there are an infinite amount of digits before the decimal in both numbers. With that, it also means, both numbers contained an unlimited amount of digits after the decimal. Thus, both infinity numbers with a fractional part are also equal to one another as of lengthwise.

For a conclusion, numbers are always the same length if they are infinity numbers.

#### The Formula

In my understanding, the general formula for calculating infinity numbers would be “Infinity equation Infinity = Infinity”. For the case of this article, I would write the general formula as the general infinity formula for calculating a mathematical multiplication equation. Thus, the general formula for calculating infinity numbers in this example would be written as “infinity x infinity = infinity”.

**General Formula: ∞ x ∞ = ∞**

For my doctrine of infinity calculation, I have two formulas for calculating mathematical equations that involve infinity numbers. The first formula is for when we are calculating infinity numbers that contain a variety of digits. This means the infinite numbers are numbers that do not only contained only one single repeating digit that runs infinitely in length. For my first formula, the formula is written as “Infinity Calculation is equal to Infinity Assumption and is equal to Infinity Alteration”. In short, I write my formula as **“infC = infA = infAL”**.

**Infinity Numbers That Contains Varieties Of Digits: infC = infA = infAL**

My second formula is a formula for calculating infinity numbers in the circumstance that the digits in the infinity numbers do not change. In another explanation, I classified this as infinity numbers that are made up by only one digit and that one digit will be repeating itself infinitely. For example, an infinite amount of nine multiply by another infinite amount of nine. To put this in context, we are assuming that we are multiplying two numbers together and each number only contains the digit nine and the digit nine will repeat itself indefinitely. For my second formula, I write the formula as “Infinity Number equation Infinity Number equal to Infinity Pattern”. For a short version, I write this formula as **“infN e infN = infP”**.

**Infinity Numbers With A Single Repeating Digit: infN e infN = infP**

#### — Formula 1: Infinity Numbers That Contains Varieties Of Digit —

**The first formula: “infC = infA = infAL”.**

When we are applying mathematical equations to infinity numbers, we would not be able to get the true final result value for the entire equation. This is because the infinity numbers will never have an ending and because the numbers will never have an end, we would not be able to get the final result value for the entire equation. Nevertheless, in my opinion, we can always get the result value for the part of the numbers where we had already seen. Thus, I labeled the result values that are produced by an equation of what we had already seen in the infinity numbers as the “State Of Infinity Result Value”.

To put this in context, if we were to receive two strings of digits that are infinite in length and we are applying a mathematical equation to the strings of digits, we would be able to get the result value for the digits that we had already received but not the result value for the entire two strings of digits. Let assume that we are receiving the same amount of digit each time for both strings. At each time when we received a new set of digits, we would be able to calculate the result value for all the digit that we had received. For a similar comparison, this would be similar to an event in time. If time was a mathematical equation, then we are experiencing the result value for what had occurred but we had not experienced or been able to see the result value for what had not occurred. In short, a “State of Infinity Result Value” is the equation’s result value of the part that we had already received and calculable within the infinite numbers.

The first formula is not just only usable for calculating numbers that are infinite in length. The first formula is applicable to circumstances where numbers are not infinite in length but are of an unknown length. In other words, very large numbers that we can’t read and apply a mathematical equation to in one time.

In a perspective, I described formula one as a formula for dealing with “Infinity Numbers That Contains Varieties Of Digit”.

#### The Properties of Formula 1

For the properties of formula one, we would have two properties, and they are “Infinity Assumption” and “Infinity Alteration”. For “Infinity Assumption”, we would also have two sub-properties and they are “Infinity Post-Assumption” and “Infinity Pre-Assumption”. With “Infinity Post-Assumption”, we have one property that only applies to a mathematical addition or a mathematical subtraction equation. The property is “Infinity Larger-Assumption”.

Property Map of Infinity Assumption:

Infinity Assumption:

**Infinity Post-Assumption:**- Infinity Larger-Assumption

**Infinity Pre-Assumption**

The amount of “State of Infinity Result Value” that we are required to produce in a mathematical equation at each part of the infinity numbers depends on the type of mathematical equation that we are dealing with.

For the “Infinity Alteration” property, “Infinity Alteration” will have one sub-property and that property is “Infinity Unchanged”. I also classified “Infinity Unchanged” as “Eternal Unchanged”. Therefore, sometime I may use the name interchangeably for this property. “Infinity Unchanged” is a property that is found within a subtraction, an addition and a multiplication equation of infinity numbers. Nevertheless, the “Infinity Unchanged” property is not found from a division equation of infinity numbers that are not made up by only one repeating digit.

Property Map of Infinity Alteration:

Infinity Alteration:

**Infinity Unchanged/Eternal Unchanged**

##### — State of Infinity Result Value —

##### Carry-Over Values and the “State of Infinity Result Value”

When we are calculating infinity numbers, often time, we would have to deal with carry-over values. The only equation that we do not have to deal with a carry-over value is a division equation. How about a subtraction equation? In the general subtraction formula, the carry-over/regrouping values would be replaced with the borrowing/regrouping values. Nevertheless, I wrote a subtraction formula to accommodate my infinity formula. In my subtraction formula, I do not use the borrowing/regrouping value but would use a carry-over value instead. For a reference to my subtraction formula, the full article for the formula can be found at Kevin’s subtraction formula.

For a summary of my subtraction formula, I use absolute values for calculating the result value at each set of digits. I do not swap the position of the numbers when the first number is the lower number but I keep the numbers in their original position. In my subtraction formula, I do not borrow a value from the next set of digits in the first number. Rather, I either add or subtract a value of one to the next set of digits in the first number, and whether to subtract or to add is bases on whether if the first number is the larger or the smaller number. Thus, in my infinity formula, carry-over values are applied to an addition, a subtraction, and a multiplication equation but not to a division equation.

When we are calculating the seeable and calculable part of infinity numbers to get the “State of Infinity Result Value” and when it comes to the carry-over values. It is very important when there is a carry-over value that produced from the equation. This carry-over value that I mentioned here is not the carry-over value from applying the equation to each set of digits within the seeable part of the infinity numbers. But is the final carry-over value from the equation of the entire seeable part of the infinity numbers.

For example, from the equation of ∞ 3787 + &infni; 7018 and we are considering that there is an infinite amount of digits that will be added to the beginning of both of the infinity numbers. We would not know what digits are going to be added to the beginning of both of the infinity numbers. Nevertheless, the seeable part of the first number is 3787 and the seeable part of the second number is 7018, and when we added the two seeable parts together, we would have an answer of 10,805. Since we added four digits to four digits and we have not completed the equation, our result value at this time should only contain four digits. Anything beyond four digits would be a carry-over value. Since infinity numbers are numbers that are infinite in length, we would not be able to be at the last digits set in the infinity numbers and the equation is an endless equation. Therefore, in the example of ∞ 3787 + ∞ 7018, when added the two seeable parts of the infinity numbers together, we would have a value of one as the final carry-over value for the equation before we are obtaining more digits from the infinity numbers. The main question here is when should we write or when should we not write this carry-over value into the “State of Infinity Result Value”?

When it comes to a true addition equation or a multiplication equation, we are always increasing the digit value of the numbers that involve in the equation. In terms, the equations would always produce equal to or larger digit values on top of the digit value of the largest numbers out of the two numbers that involved in the equation. In this type of equation, because we are always adding digit values on top of digit values, writing down the carry-over values into the “State of Infinity Result Value” for any part of the equation without applying the carry-over values twice will not alter the next “State of Infinity Result Value” in a way that the value will be an incorrect value. For example, if I was to add 1357 + 1701 and I only want to add 357 + 701 before adding the two 1s together, I would get a result value of 1058. I can write the result value as is 1058 and then add this result value to the result value of the two one. Which can also be written as 1000 + 1000 + 1058, of which, would be equal to 3058. When this principle is applied to equations of infinity numbers, the same property would also apply to the “State of Infinity Result Value”. In the example of ∞ 357 + ∞ 701, at this part in the numbers, it would make more sense if we were to write the “State of Infinity Result Value” as 1058. Rather than writing the value as 058. Therefore, in a conclusion, the final carry-over value of the current part in the infinity numbers during an addition and a multiplication equation should be written down into the “State of Infinity Result Value”.

When I describe in regard to a true addition equation, I define a true addition equation as an addition equation that in final will always increase the values of the numbers that involved, and is not an addition equation where the equation turned into a subtraction equation due to the differential in the negative or the positive base of the numbers. This can be similar to when I describe in regard to a true subtraction equation, I describe a true subtraction equation as a subtraction equation that truly reduces the value of the first number to the value of the second number, and is not a subtraction equation that turned into an addition equation due to the differentials of the negative or the positive base between the two numbers.

When we come to the carry-over value for a true subtraction equation, the property of the carry-over value does change. In a true subtraction equation that involves two numbers, we are reducing the digit value of one number to another number. From my formula, the carry-over value that produced from a sub-equation of a digit sets in the numbers has to be added to or subtracted from the next set of digits in the first number. Thus, we can not write the final carry-over value from a subtraction equation of the current seeable part of the infinity numbers into the “State of Infinity Result Value”. This is because we have not seen the next set of digits to able to apply the carry-over value to. This property would also apply in the circumstance where we were to use the general subtraction formula to calculate the infinity numbers. We can’t write down the borrowing value either, simply because we can’t borrow from what we can’t see or a nil value. Therefore, in conclusion, in a subtraction formula of infinity numbers, the final carry-over value of the current seeable part of the infinity numbers can not be written into the “State of Infinity Result Value”. This is because the value is to be applied to the next set of digits, or to the equation of the next set of digits and is not a true result value when applying alone. Applying the carry-over value to the “State of Infinity Result Value” without any set of digits will produce an incorrect result value. This is simply because we are carrying a value to a value that we have not seen.

Subtraction is also the one part of the infinity formula that seems to not make sense at first glance. Nevertheless, by looking at an example we can understand more. For example, if we were to use my subtraction formula for an equation of 3384 subtract to 2554 and I only want to subtract 384 to 554 before subtracting the final digits set of 3 from the first number to the final digits set of 2 in the second number. We would get a result value of 830 and a carry-over value of 1. If we were to write down the result value for this state as 1830, it would not make sense. Also, if we wrote the result as 1830, we would not be able to apply the result value to next set of digits. If we didn’t write down the final carry-over value, we can write the equation as (3000 – 1000) – 2000 + 830, of which will give us the correct answer of 830. Now, if we were to write down the final carry-over value into the result value from the last equation before we process the last set of digits, we would have 3000 – 2000 + 1830. From which, would give us 2830 as a result value for the equation. Nevertheless, that is not the correct result value and if we were to write the equation as 3000 – (2000 + 1830), we would get -830 as the result value for the equation. Of which, wouldn’t be the correct value either.

If we were to treat the above example as infinity numbers, we can write the equation as ∞384 – ∞554. In this circumstance, if we are assuming that the first number is going to be the larger number, we would have ∞830 as the “State of Infinity Result Value” or simply 830. On the other hand, if we are going to assume that the second number is going to be the larger number, we would have ∞170 as the “State of Infinity Result Value” or simply 170. In both of our assumptions and whether if the first number is the larger number or not, we would still have a carry-over value that we would have to carry to the equation of the next seeable part of the numbers. To put this theory into a practical application, with the example of the first number being the larger one, We can have 18,384 – 3,554, of which, would give us 14,830 as a result value. For an example of the second number being the larger number, we can have 18,384 – 38,554 and the result value of the equation would be -20,170.

When it is a division equation, we wouldn’t have a carry-over value. This is because in a division equation, whether at any part in the numbers, we would have to divide all the digit from the first number to all the digit from the second number to get a result value. Therefore, in an infinity division equation, at each time when we received a new set of digits that increase the seeable part of the infinity numbers. We would have to divide all the seeable digits in the first number to all the seeable digits in the second number. We wouldn’t be able to divide part of the numbers to each other and somehow manage the result value from one part of the numbers to the result value from another part of the numbers to produce a correct result value for the entire equation. Therefore, during an infinity division equation, at any time we are obtaining a new set of digits in the infinity numbers, it is going to be a completely new equation. Hence, there wouldn’t be any value that is going to be applied to the later or the previous equations. However, there is a remainder value. Nevertheless, the remainder value and how many decimal places are we going to use is up to our decision at the beginning instance of the equation, and this would be different between each case.

##### — Infinity Assumption —

When we are calculating a mathematical equation’s value for numbers that are infinite in length, at each time when we receive a new set of digits, we would have to assume that the set of digits that we had just received is the last set of digits within the numbers string. With that assumption, we would calculate the result value for all the digits we had gotten from the string of infinity numbers and assume that the result value is the final result value for our equation even though the result value can never be the final result value. Since the strings of numbers that we are operating on are infinite in length. Thus, our assumption would also be infinite in the amount.

On one hand, we are assuming that the set of digits we had just read from the infinity numbers are the last set of digits. On the other hand, we know that infinity numbers are numbers that are infinite in length. Thus, besides having to infinitely assume that the digits that we are getting are the last set of digits from the strings of infinite numbers. We would also have others assumption to make to be able to calculate the result value for all the possibility of what could be the ending or the beginning of the numbers. Other than that, we would also have to consider the possibility that we are receiving/reading the digits in the infinite numbers starting from the tail end or starting from the front end.

**Infinity Post-Assumption**

Infinity Post-Assumption is when we are assuming that we are reading the digits in the infinity numbers starting from the tail end of the numbers. By assuming that we are reading the digits starting from the tail end, the majority of our mathematical equation that is going to be applied to the infinity numbers would be the same as our daily life mathematical calculation. This is because, in our daily life mathematical calculation, we would calculate a mathematical’s result value for numbers starting from the end or the right side of the numbers. If we were going to calculate the result of a mathematical equation manually using a regular mathematical method, from the right side to left side is also the method of how we would write the result value that is not a division equation on paper.

When we are assuming that we are reading the infinity numbers from the tail end, there is another assumption that we would have to make. That assumption is if the infinity number that we are dealing with is a number that is positive in value or negative in value. We would never know if the infinity numbers would contain a positive or negative sign until we reach the beginning of the numbers. For a number that is infinitely in length, that would be an impossible thing to evaluate. Therefore, under “Infinity Post-Assumption”, we would always have to assume the circumstances that the infinity numbers can be either be positive or negative in value.

Thus, with “Infinity Post-Assumption”, and when applying a mathematical equation to the infinity numbers, we would have to produce different answers for all the possibility that involves. When it comes to how many result values that have to be produced for all the possibility that associates with Infinity Post-Assumption, it would be based on the type of mathematical equation that is being applied to the numbers. The amount of result value that we would have to produce for a multiplication equation would differ from the amount of result value that needed to be produced for an addition formula.

Within Infinity Post-Assumption, we would have a sub-property of Infinity Post-Assumption. The property would be “Infinity Larger-Assumption”. When we are working with infinity numbers, although it is true that both numbers are infinitely in length, we would also have to assume that one number can be larger than the other by digit value. The reason of why one infinity number could be larger than the other infinity number is because we could never read the final digit in both of our infinity numbers, which in this case would be the first digit in both numbers, and the first digits of both numbers could be any digit. Thus, although both numbers are equal in length, as long as we haven’t read the first digit in both numbers, either number could be the larger number. “Infinity Larger-Assumption” is a property of “Infinity Post-Assumption” and “Infinity Larger-Assumption” only attach to an infinity addition or an infinity subtraction equation.

**— The Amount of “State of Infinity Result Value” for “Infinity Post-Assumption” —**

**Multiplication: ** For a multiplication equation between two infinity numbers and when we are assuming that we are reading the infinity numbers starting from the back of the numbers, we would not know if the infinity numbers are negative or positive in value. This is because we have not seen the beginning of the numbers. Also, we would never be able to see the beginning of the numbers because they are infinity numbers and infinity numbers are infinite in length. Therefore, we would have to assume that the first number can either be negative or positive in value and that principle would also apply to the second number.

From all the possible combination of which number could the be the negative number or which number could be the positive number, we would have four possible combinations. We can have the first number and the second number as both positive numbers or they are both negative numbers as two possible combinations. For the third possible combination, we can have the first number being the positive number and the second number being the negative number. With the fourth possible combination, we can have the first number being the negative number and the second number being the positive number.

Although we have four possible combinations of which number is the negative or the positive number, nevertheless, the equation only need to produce two result value. This is because of the property of a multiplication equation. The property of a multiplication equation for a normal number is when two positive numbers multiply to each other, the equation would produce a positive result value. Positive result values also are result values that would be produced from a multiplication equation that involves two negative numbers. The only time when a multiplication equation produces a negative result value is when two numbers are not the same in the negative or positive base. Therefore, we can safely assume that whether the two infinity numbers can be anything when it comes to the negative or positive value, we would only have to produce two “State of Infinity Result Value” for all the possible combination of whether the first number is positive or negative in value combine with the possibility that if second number is a positive or a negative number. This two “State of Infinity Result Value” for a multiplication equation of infinity numbers of “Infinity Post-Assumption” are the exact same in digit’s value, they are only difference

by the negative or the positive sign.

In the event of a multiplication equation between two numbers, we do not have to worry about which number can be the larger number. This is because whether which numbers is the larger number, the final answer for the entire equation would still be the same.

The map below described the possibilities that attach to each “State of Infinity Result Value” for a multiplication formula of infinity numbers that associates with “Infinity Post-Assumption”.

“State of Infinity Result Value” 1: (A & B = +) or (A & B = -)

“State of Infinity Result Value” 2: (A = +, B = -) or (A = -, B = +)

In conclusion, we would require two “State of Infinity Result Value” for the “Infinity Post-Assumption” property of a multiplication equation for two infinity numbers.

**Addition:** When it comes to an addition formula for two infinity numbers and we are assuming that we are reading the numbers starting from the tail end, the amount of “State of Infinity Result Value” that the equation need to produce is different from a multiplication equation. In an addition formula, if we are adding two numbers that have the same negative or positive base then we are adding the numbers together and the result value would have the same negative or positive base as the two numbers. On the other hand, if we are adding two numbers that are different in the negative or the positive base then we are subtracting the first number’s value to the second number’s value and the result value of the equation would be the same in the negative or positive base as the larger number out of the two numbers.

When we are assuming that we are reading the infinity numbers starting from the back, we would not know if the numbers are negative or positive in value, or which number is the larger number. Therefore, the first assumption we have to make is assuming all the possibility surrounding the negative and the positive value for both numbers. When it comes to negative or positive values, there are four possibilities for adding two numbers together. The first possibility is the first number is a positive number and the second number is also a positive number. For the second possibility, both of the numbers are negative numbers. With the third possibility, we can have the first number as a positive number and the second number as a negative number. In a final and is a fourth possibility, our first number is a negative number and our second number is a positive number.

With the first and second possibility when both numbers are the same in the negative or the positive base, we do not have to assume which number can be the larger number. This is because the procedures for the addition equation would not change whether which number is the larger number. However, when it comes to when the numbers are different in the negative or the positive base, the procedures for the addition equation would change base on which number is the larger number. The addition equation for adding two numbers that are different in the negative or the positive base is similar to a subtraction equation. Thus, if you need more information on the subtraction formula that associate to my infinity formula, please refer to my mathematical subtraction formula.

With the above in context, for an addition formula of infinity numbers, “Infinity Post-Assumption”‘s property would require a total of six “State of Infinity Result Value”. The first “State of Infinity Result Value” would be for the possibility that both numbers are positive numbers. The second “State of Infinity Result Value” would be for the possibility that both numbers are negative in value. These first two “State of Infinity Result Value” would exactly be the same in digit value. Nevertheless, they are different by the negative or positive sign.

When it comes to the possibility that the first infinity number is a positive number and the second infinity number is a negative number, we would have to produce two “State of Infinity Result Value”. The third “State of Infinity Result Value” would attach to the possibility that the first number is the larger number. With that, the fourth “State of Infinity Result Value” would attach to the possibility that the first number being the smaller number.

The fifth “State of Infinity Result Value” is for the possibility that the first infinity number is negative in value and is larger than the second infinity number, which is a positive number. The sixth “State of Infinity Result Value” is attached to the possibility that the first infinity number is negative in value and is smaller than the second infinity number, which would be a positive number.

The third and fifth “State of Infinity Result Value” are the same in digit value but they are different in the negative or positive base. The fourth and sixth “State of Infinity Result Value” are exactly the same as of digit value, nevertheless, their differences are by the positive or negative sign. The map below described the possibilities that attach to each “State of Infinity Result Value” for an addition formula of infinity numbers that associates with “Infinity Post-Assumption”.

“State of Infinity Result Value” 1: (A & B = +)

“State of Infinity Result Value” 2: (A & B = -)

“State of Infinity Result Value” 3: (A = +) & (B = -) & (A > B)

“State of Infinity Result Value” 4: (A = +) & (B = -) & (A < B)

“State of Infinity Result Value” 5: (A = -) & (B = +) & (A > B)

“State of Infinity Result Value” 6: (A = -) & (B = +) & (A < B)

In conclusion, there would be six “State of Infinity Result Value” for the property of “Infinity Post-Assumption” that attach to an addition equation for two infinity numbers that vary in digits.

**Subtraction:** In context, the properties that associate with a mathematical subtraction equation does seem to share some common characteristic as the properties that associate with an addition equation. Nevertheless, there are noticeable differences between the two properties of the two equations.

In a subtraction equation, when we are subtracting two numbers that are the same in the negative or positive base then we are subtracting the first number’s value to the second number’s value. When the first number is larger than the second number by digit value then the result value of the equation would be in the same negative or positive base as the two numbers. In the circumstance that the first number is smaller than the second number by digit value then the result value from the equation would have the negative or positive base that is opposite from the two numbers. For example, from the equation of (+A – +B) and (A > B), the equation would produce a positive result value. For another example, from this equation of (+A – +B) and (A < B), the would produce a negative result value.

When we are subtracting two numbers that are not the same in the negative or the positive base then we are adding the digit value of the second number to the first number. The result value from the equation would always have the same negative or positive base as the first number. For example, from the equation of (+A – -B), the equation would always produce a positive result value, and it does not matter if A is larger than B or not.

With the above in context, there would be six “State of Infinity Result Value” for the property of “Infinity Post-Assumption” of a subtraction equation for two infinity numbers. The first “State of Infinity Result Value” is for the possibility that the first number is larger than the second number by digit value and both numbers are positive in value. With the second “State of Infinity Result Value”, the value is attached to the possibility that both numbers are positive in value and the first number by digit value is the smaller number. For the third “State of Infinity Result Value”, the value serve the probability that both numbers are negative numbers and the first number would be the larger number by digit value. Just like the third one, the fourth “State of Infinity Result Value” is for the probability that both numbers are negative numbers, nevertheless, the first number would now, in digit value, be the smaller number.

In the fifth “State of Infinity Result Value”, the value is attached to the possibility of when the first number is a positive number and the second number is a negative number. Finally, onto the final and is the sixth “State of Infinity Result Value”, the value serves the probability of when the first number is a negative number and the second number is a positive number.

The map below described all the possibility that attaches to each “State of Infinity Result Value” for a subtraction formula of infinity numbers that associates with “Infinity Post-Assumption”.

“State of Infinity Result Value” 1: (A & B = +) & (A > B)

“State of Infinity Result Value” 2: (A & B = +) & (A < B)

“State of Infinity Result Value” 3: (A & B = -) & (A > B)

“State of Infinity Result Value” 4: (A & B = -) & (A < B)

“State of Infinity Result Value” 5: (A = +) & (B = -)

“State of Infinity Result Value” 6: (A = -) & (B = +)

With the “State of Infinity Result Value” from above, the first and third “State of Infinity Result Value” are the exact same when it comes to digit value, nevertheless, one of them would be negative in value and the other would be positive in value. The digit value of the second “State of Infinity Result Value” is absolutely the same as the digit value of the fourth “State of Infinity Result Value”. However, a positive sign would be attached to one value while the other would have a negative sign attached to. When it comes to the fifth and the sixth “State of Infinity Result Value”, it is no doubt that they are unequivocally the exact same in digit value, nonetheless, there is one feature that will separate them apart and that feature is which value is the positive one and which is the negative one.

In conclusion, we would require six “State of Infinity Result Value” for the property of “Infinity Post-Assumption” in a mathematical equation that involves two infinity numbers.

**Division:** In a division equation, when it comes to how many “State of Infinity Result Value” we are required to produce when we are assuming that we are reading the infinity numbers from the tail end, it would be similar to a multiplication equation of infinity numbers. We would have to assume all the possibilities of whether either infinity number is negative or positive in value. There are four possibilities between the two numbers when it comes to the combination of whether which number is the negative or the positive number. First, both numbers are positive numbers. Second, they are both negative numbers. Third, the first number is a positive number and the second number is a negative number. Fourth, the first number is negative in value and the second number is positive in value.

The property for a mathematical division equation of infinity numbers would similarly be the same as a division equation of normal numbers. When both numbers in a division equation have the same negative or positive base, the result value that produced from the equation would be a positive result value. The only time when a division equation produces a negative result value is when the two numbers that involved in the equation are different in the negative or positive base. When looking at the four possibilities of all the combination of whether the first number is the negative or the positive number combine with whether the second number is the negative or the positive number, it seems that we would require four “State of Infinity Result Value”. Nevertheless, when we are combining the explanation of all the possibility that attach to a division equation of infinity numbers for the event of when we are assuming that we are reading the numbers from the back with the explanation of the property of a division equation, the true reality is we only need to produce two “State of Infinity Result Value” for all four possibilities. Thus, we would require two “State of Infinity Result Value” for when we are assuming that we are reading the infinity numbers starting from the end of the numbers. These two “State of Infinity Result Value” are the same in digit values, nevertheless, they are different by the negative or the positive sign.

The map below described the possibilities that attach to each “State of Infinity Result Value” for a division equation of infinity numbers that associates with “Infinity Post-Assumption”.

“State of Infinity Result Value” 1: (A & B = +) or (A & B = -)

“State of Infinity Result Value” 2: (A = +, B = -) or (A = -, B = +)

In conclusion, for a division equation of infinity numbers, we are required to produce two “State of Infinity Result Value”.

**Infinity Pre-Assumption:**

In my explanation, “Infinity Pre-Assumption” is when we are assuming that we are reading the digits in the infinity numbers starting from the beginning of the numbers. Which in context can be explained as reading the digits within the numbers starting from the first digit on the left toward the last digit on the right, or simply reading the numbers from left to right. With “Infinity-Pre-Assumption” we do not need to assume if the infinity numbers are numbers that can either be negative or positive in value. Also, when it comes to a subtraction or an addition equation that require the knowledge of which number is the larger number, we do not have to assume whether which number is the larger number. This is because when we are assuming that we are reading the digit from the beginning, we are also assuming that we have seen the first digit and therefore, we already know which number is the larger or the smaller number.

Thus, when applying any mathematical equation to infinity numbers and we are assuming that we are reading the numbers starting from the beginning of the numbers, we would only need to produce one “State of Infinity Result Value”. Hence, in conclusion, whether any type of mathematical equation of infinity numbers, only one “State of Infinity Result Value” is needed to be produced for the property of “Infinity Pre-Assumption”.

**Conclusion Of Infinity Assumption:**

In conclusion, when I define infinity calculation equal to infinity assumption. It can be explained as when we are calculating the infinity numbers, although we know that it is not and can never be the final seeable part of the numbers, each and every instance when we stop to calculate all the seeable part of the numbers, we are still assuming that it is the final seeable part of the numbers that we are calculating. This is why we stopped and calculate a result value for the equation. Nevertheless, with the knowledge that the seeable parts in the numbers can extend, we would always treat the calculation as a continuous calculation.

In a real world case, if there was another civilization in another world beyond our planet that sending us two strings of digits that of an unknown length. We would not know if it is the beginnings that we are receiving or is it the endings that we are reading from. Thus, if we truly wanted to calculate the string of digits at the same time at when we are receiving them then we would need to produce result values for all the possibilities that are associated with both numbers. Thus, in “Infinity Assumption”, we have “Infinity Post-Assumption”, it’s sub-properties, and “Infinity Pre-Assumption”.

In this example of another civilization, the reason of why we would want to calculate the strings of digits at the same time at when we are receiving the digits is because we would not know how large the numbers are. They could be numbers that so large and seem like infinitely in length or they could truly be infinity numbers. Also, we might not know for sure which planet is sending us the strings of digits. Take into consideration, if the civilization that sending us the strings of digits is 1 billion light years away, and that string of digits took 3 billion years to travel to our planet, and also, with the possibility that those strings of numbers can run for one more minute or for another 1 billion years. Should we really wait until we receive all the digits and then start the equation? If there is a message within the mathematical numbers, would we really want to take a risk and wait one billion more years or forever to then calculate a result value for the equation? Besides the example scenario, I do believe there would be others scenario where we do actually require to calculate numbers that are in an unknown length at the same time at when we are reading the numbers.

When calculating an equation’s result value of numbers where we don’t know the ending, the beginning or where did we started from then we should also prepare all the possible result values for the equation. By having all the possible result values, if we do ever reach the ending or the beginning of the numbers then without recalculating or rereading the entire numbers, we would almost instantly have the result value for the entire equation from one out of all the possible result values. The almost same scenario would apply to infinity numbers. Except, in infinity numbers, it is more important than ever to have all the possible result values. This is because we can never reach the ending or the beginning so we can only assume that one out of all of the possible result values is the result value for the entire equation. Nevertheless, we would never truly know which one out of all of the possible result values is the actual result value for the entire equation of infinity numbers. However, we know for sure that we do have the actual result value for the entire equation from that pool of all of the possible result values.

For how many possible result values that a mathematical equation of infinity numbers needs to produce is always bases on the type of the mathematical equation. On another subject, like mentioned previously, I defined the result value of the equation for when we stopped in the infinity numbers to calculate the seeable parts as the “State of Infinity Result Value”. Thus, we can also classify all the possible result values as all the “State of Infinity Result Value” that associate with “Infinity Assumption”. With the explanation, the map below declared how many “State of Infinity Result Value” that a mathematical equation is required to produces for when we are calculating infinity numbers.

**Multiplication Equation:** For a multiplication equation, the equation needs to produces 2 “State of Infinity Result Value” for the property of “Infinity Post-Assumption” and 1 “State of Infinity Result Value” for the property of “Infinity Pre-Assumption”. Thus, 3 “State of Infinity Result Value” is produced at each time when we chose to stop in the infinity numbers to calculate a result value for what we had already seen.

**Division Equation:** When it comes to a division equation, the equation would require 2 “State of Infinity Result Value” for the property of “Infinity Post-Assumption” and 1 “State of Infinity Result Value” for the property of “Infinity Pre-Assumption”. Therefore, 3 “State of Infinity Result Value” would be produced by the equation at each time when we decide to halt the reading of the infinity numbers to calculate a result value for the seeable parts.

**Addition Equation:** Attaches to an addition equation, the equation has 7 “State of Infinity Result Value” for the event of when we declared a pause in reading from the numbers to calculate what we had already read. 6 “State of Infinity Result Value” would be for the property of “Infinity Post-Assumption” and 1 “State of Infinity Result Value” would be for the property of “Infinity Pre-Assumption”.

**Subtraction Equation:** Just like an addition formula, a subtraction formula of infinity numbers should always produce 7 “State of Infinity Result Value” for every instance of when we declared that we should interrupt the reading and start calculating a result value for all of what was read. From the 7 “State of Infinity Result Value”, 1 is for the property of “Infinity Pre-Assumption” and 6 are for the property of “Infinity Post-Assumption”.

#### Infinity Alteration:

In my explanation, while calculating the result value of a mathematical equation for infinity numbers, what we would get is the “State of Infinity Result Value”. By looking at the procedures that we would have to make in a mathematical infinity calculation, we would further understand the property of the “State Of Infinity Result Value”. Generally, every time when we read a new set of digits from the infinity numbers, we would either calculate all the seeable digits of the infinity numbers all together in one time, or we simply calculate the result value for the set of digits we had just read and then we would add that result value to the result value that we had from before reading this new set of digits. The total result value of the equation of what we had for the entire infinity calculation, including the set of digits that we just read would be the “State of Infinity Result Value”.

With that, we can see that each time when we read and calculate a new set of digits from both numbers, the “State Of Infinity Result Value” would always change. Inside the “State Of Infinity Result Value”, in some instance, there are digits that will never change, including their location within the “State Of Infinity Result Value”. Nevertheless, one thing we know for a fact, and that is, the total value of the “State Of Infinity Result Value” would constantly change and would most likely not be the same. Thus, the result value for an equation that applies to infinity numbers will almost always be a changing result value. Therefore, the result value for an equation that applies to infinity numbers can be classified as a result value that would always change or alter, in others word, “Infinity Alteration”.

There are equations of infinity numbers that the property of “Infinity Alteration” does not apply to. Those equations that are not applied by the “Infinity Alteration” property are some of the equations that involve infinity numbers that contain only one indefinitely repeating digit.

Within the property of “Infinity Alteration”, there is a sub-property, and the sub-property is the “Infinity Unchanged” property. I also labeled the “Infinity Unchanged” property as the “Eternal Unchanged” property.

Although we know that the “State Of Infinity Result Value” would almost always alter while we are calculating an equation’s result value for the infinity numbers. Nonetheless, when it comes to examining the already calculated “State Of Infinity Result Value”, there are instances of when the calculated “State Of Infinity Result Value” does contain an amount of digit that would not alter through time. Those digits will remain unchanged indefinitely even if we are adding an infinite amount of digit to the infinity numbers. As we progress through calculating the infinity numbers, the amount of digit within the “Infinity Unchanged”‘s value would increase. Nevertheless, the digits that are already contained within the “Infinity Unchanged”‘s value and their order will eternally remain unchanged.

When calculating infinity numbers, the “Infinity Unchanged” property is found from mathematical equations of multiplication, addition, and subtraction. Nonetheless, there isn’t an “Infinity Unchanged” property within a division equation of infinity numbers when the infinity numbers are numbers that contain only one indefinitely repeating digit. In a perspective, I would classify that with a division equation of infinity numbers that do not contain only a single indefinitely repeating digit, the equation will almost always produce a true “Infinity Alteration” “State of Infinity Result Value”. This is because in a division equation when there is a new digit that is going to be added to both the numbers that involve in the equation then the result value from the equation would almost always to completely be differed than the previous result value. This is because, in a division equation, it is not possible to calculate just part of the numbers then after calculate another new part that would be added to the numbers. Thus, when there is a new digit that going to be added to both infinity numbers in a division equation, we would have to re-calculate the result value by dividing all the digits in the first number to all the digits in the second numbers.

**Addition and Infinity Unchanged for Infinity Post-Assumption:**

For an addition formula property, of when we are processing the equation starting with the ending digits and calculating toward the beginning digits. For each time of when we are adding two sets of digits together from both numbers. We would have to keep track of the carry-over value. If there is a carry-over value from an equation of the two digit sets then the carry-over value would be applied to the equation of the next sets of digits that are on the left of the current sets of digits. Any result values from an equation that is proceeding the equation of the current sets of digits can be modified by a carry-over value. Nonetheless, we would never have to go back to the result values that had already been processed by the equation. Therefore, if we were to apply an addition equation to two sets of digits, and we were to process the numbers by a set amount of digits at a time, and we were to process the equation starting from the rightmost digits in the numbers, we would never have to modify any result values that had already been processed by the equation.

When applying the addition equation to infinity numbers, the property of a carry-over value does not change. Therefore, as we are processing the addition equation for two infinity numbers, the “State Of Infinity Result Value” would constantly increase in length. Nonetheless, after being added to the “State of Infinity Result Value”, whether if it is the order or the digits themselves, the digits of the “State of Infinity Result Value” will never alter. There is one exception to this case and that exception is the carry-over value from the equation of the current sets of digits. In a case of an infinity addition equation of when we are assuming that we are processing the equation starting with the rightmost digits of the numbers, we should always write down the carry-over value from the equation of the current sets of digits into the “State of Infinity Result Value”. In my opinion, for an addition equation, although, we have not processed the equation for the next sets of digits, the “State of Infinity Result Value” would make more sense with the carry-over value from the equation of the current sets of digits being written in than without.

Thus, when there is a carry-over value from the equation of the current sets of digits, which in this case is the leftmost digit of the “State of Infinity Result Value”, that digit is not an “Infinity Unchanged” value. The reason of why is because our infinity addition equation is a continues equation that is endless, and since we haven’t processed the equation of the next sets of digits, the carry-over value from the equation of the current sets of digits is not a true result value but is a value that would be applied to the equation of the next sets of digits. Therefore, when there is a carry-over value from the equation of the current sets of digits, any digits that are not that carry-over value within the “State of Infinity Result Value” are the “Infinity Unchanged” value.

In conclusion, in an infinity addition formula of when the equation’s process takes on the assumption that the equation is starting with the digits from the rightmost of the numbers, an “Infinity Unchanged” value is all the digit within the “State of Infinity Result Value” that is not the carry-over value of the equation of the current sets of digits.

**Addition and Infinity Unchanged for Infinity Pre-Assumption:**

For an infinity addition equation of when we are assuming that we are processing the equation starting from the leftmost digits of the numbers, there would still be an “Infinity Unchanged” property that attaches to the equation. Nevertheless, in this scenario, obtaining the “Infinity Unchanged” value can be a bit tricky. The reason behind the complication for obtaining the “Infinity Unchanged” value is caused by the property of the carry-over value that is associated with an addition equation. When it comes to the property of a carry-over value of an addition equation, if there is a carry-over value from the equation of the current sets of digits then the carry-over value will always be applied to the equation of the sets of digits that are on the left of the current sets of digits. In a normal circumstance, where the addition equation process the numbers starting from the rightmost digits toward the leftmost digit, the carry-over value of an equation of two sets of digits within the numbers would always be applied to the equation of the next sets of digits. Nevertheless, since we are processing the equation starting from the leftmost digits toward the rightmost digits, this would be a reverse order, where the carry-over value will modify what our addition equation had already processed.

In this situation of when the addition equation process the digits in a reverse order. There is one property that attaches to the carry-over value of an addition equation that can ease our process for obtaining the “Infinity Unchanged” value, and that is the carry-over value can never be larger than one if it is only two sets of digits that we are adding together. For example, if the equation is processing one digit at a time and we are adding a digit 9 to another digit 9. From that procedure, we would get a result value of 18. From the result value, the carry-over value is the leftmost digit, which is the digit 1. The rightmost digit 8 would be the result value of that procedure. In this example, there is not another digit that would be larger than the digit nine to give the equation the capability to produce a carry-over value of two, it is not possible.

For another example, if the addition equation was set to process at the rate of two digits at a time, and we are adding two sets of digits together. For this example, one of the digits set contained 99 and the other set also contained 99. From the equation of the two sets of digits, we would get a result value of 198. From the result value of this equation, we would have the digit 1, which is the leftmost digit as the carry-over value. The other digits that are the 9 and the 8, when combined as 98 is the result value of this equation.

After the examples, when examing the property of an “Infinity Unchanged value, we know that “Infinity Unchanged” values are none changing values within the “State of Infinity Result Value”. As we process through the equation, an “Infinity Unchanged” value will grow and more digit will be added to the value, nevertheless, once a digit is added to an “Infinity Unchanged” value, its position from the starting point and the digit itself will never change. Thus, the digits within an “Infinity Unchanged” value can be classified as digits that can never be modified by future procedures of the equation. Thus, we can only obtain an “Infinity Unchanged” value from a part in the result value that is safe from being modified by any future procedures.

In an addition equation of when the equation processing the digits in a reverse order, there is a probability that a carry-over value that is coming from future equations of future sets of digits would come around and modify one, many, or all the result values of the past equation of the past sets of digits. Therefore, to find the “Infinity Unchanged” value from the “State of Infinity Result Value”, every time we completed an equation between two sets of digits, we would evaluate the result value from the equation of the current sets of digits. If the result value of the equation of the current sets of digits even when being modified by a carry-over value will not produce a carry-over value, then all the result values from previous equations of previous sets of digits are the “Infinity Unchanged” value.

In an addition equation, to be able to find a value that even when being modified by a carry-over value will not be able to produce a carry-over value, we can examine the property that the carry-over value can never be greater than a value of one for an addition equation of two sets of digits. By knowing this, we know that any values that are less than the maximum digit value that the set of digits can hold are values that are not capable of producing a carry-over value when being modified by a carry-over value. For example, if we process an addition equation at the rate of one digit at a time, then our sets of digits can contain only one digit. The maximum value that the set of digits can hold in this circumstance is a 9. Beyond the 9, we would have a carry-over value. Therefore, if we were to add the largest carry-over, which is a value of one to the 9, then the 9 would turn into a 0, and we would get a carry-over value of 1. Nonetheless, any other value that is one digit and that is not the digit 9, would not be able to produce a carry-over value when added to the largest carry-over value. For another example, if our addition equation was processing two digits at a time. Then our sets of digits can contain a maximum value of 99. Any other value that is two digits and that is not 99, when combining with the largest carry-over value, would not be able to produce a carry-over value.

When adding digit values to the “Infinity Unchanged” value in an infinity addition equation where the equation is being processed in a reverse order, the values from the “State of Infinity Result Value” that became the “Infinity Unchanged” value would be added to the “Infinity Unchanged” value in the order from left to right, with the first digit being the leftmost.

In conclusion, in an infinity addition equation with the “Infinity Pre-Assumption” property, when the result value of the equation of the current sets of digits can not produce a carry-over value even when added to a largest carry-over value, then the “Infinity Unchanged” value is all the value within the previous “State of Infinity Result Value” that are not already been added to the “Infinity Unchanged” value.

In this example below, we will not get an “Infinity Unchanged” value unless the result value of the equation of the next sets of digits is anything else that is not a nine. This is because if a carry-over value is produced from any future result value, then the carry-over value will modify all the previous result values of the equation and turn the complete string of nines into zeroes. After that, the equation would also add a digit one to the beginning of all the would be zero.

1111111111∞ +8888888888∞ ---------- 9999999999

In this example below, since the last result value that we got in our “State of Infinity Result Value” is a seven which is not the maximum value for our digits set, therefore, all the digits before the seven would be the “Infinity Unchanged” value. Doesn’t matter how many digits that would be added to the right side of the two infinity numbers that are in the equation. All the digits that are not the seven in the “State of Infinity Result Value” as of now would never alter.

23587523∞ +27542434∞ -------- 51129957∞

**Addition and Infinity Unchanged of When The Values Turned The Equation Into A Subtraction Equation:**

There are instances of when an addition equation will turn into an equation that is similar to a subtraction equation. In events of when the addition equation process two numbers that are not the same in the negative or positive base, then the addition equation instead of adding values would then subtract the value of the first number to the value of the second number. There are differences between the properties of an addition equation that turned into a subtracting of values equation. Nonetheless, the properties of the “Infinity Unchanged” value for the addition equation that turned into a subtraction equation does share some similarity to the properties of the “Infinity Unchanged” value of a true subtraction equation. Thus, the information for the properties of the “Infinity Unchanged” value of an infinity addition equation where the equation turned into a subtracting of values equation can be referred to in the section of “Subtraction and Infinity Unchanged for Infinity Post-Assumption”, and also the other section with the name “Subtraction and Infinity Unchanged for Infinity Pre-Assumption”.

When subtracting a value to a value, the procedures of a true subtraction equation are exactly the same as an addition equation where the equation turned into a subtraction equation. Nonetheless, the difference between the two equation lies with the property of negative or positive values. In an addition equation when the first number is not the same in the negative or positive base as the second number then the equation would subtract the digit value of the first number to the digit value of the second number. If the first number is the larger number, then the result value of the equation would be in the same negative or positive base as the first number. Otherwise, the result value of the equation would share the same negative or positive base as the second number.

**Subtraction and Infinity Unchanged for Infinity Post-Assumption:**

In a subtraction equation of when we are assuming that we are processing the equation starting with the rightmost digit in the numbers and if we were to utilize my subtraction formula, then the properties of the subtraction equation would share some similarities to an addition equation. For a summarize of my formula, each time when we process an equation for two sets of the digits from both numbers, we would keep track of the carry-over value. How to apply the carry-over value to the equation or how does the equation produced a carry-over value are based on which number is the larger number. In my formula, I do keep track of which number is the larger number, nevertheless, my formula never swaps the position of either number.

In regard to if the carry-over value should be written down into the “State of Infinity Result Value”, it is very important in an infinity subtraction equation. As mentioned in the previous section of this article in regard to the carry-over value and an infinity subtraction equation, we know that in a subtraction equation of infinity numbers, we do not write down the carry-over value into the “State of Infinity Result Value”. This is because the carry-over value is strictly to be applied to the value of the next digits set in the first number that is on the left of the current sets of digits of where the equation is processing. If this carry-over was to be written down into the result value without being applied to the next digits set in the first number, then the result value will not make sense. Therefore, when we stopped to calculate the “State of Infinity Result Value” in an infinity subtraction equation, we never write the carry-over value into the “State of Infinity Result Value” without applying it.

Besides the difference of if the carry-over value should be written down into the “State of Infinity Result Value”, a subtraction equation does share one exact same property as an addition equation. That property is the carry-over value is always to be applied to the equation of the sets of digits that are the next left of the equation of the current sets of digits. Therefore, when the equation is going from right to left, any result values from a sub-equation between the sets of digits of the two numbers that had been processed by the subtraction equation is always safe from future modification by any procedures or carry-over values. Thus, if the assumption is that the digits in the infinity numbers are being read from right to left, then every digit within the “State of Infinity Result Value” from an infinity subtraction equation is the “Infinity Unchanged” value.

From the above, I concluded that the “Infinity Unchanged” value for an infinity subtraction equation with the property of “Infinity Post-Assumption” will always be the “State of Infinity Result Value”.

**Subtraction and Infinity Unchanged for Infinity Pre-Assumption:**

In a subtraction equation, when it comes to processing the equation starting from the left of the numbers toward the right of the numbers, it is almost similar to an addition equation that is in the same category. Nevertheless, there are some differences due to the property of a subtraction equation. When dealing with a subtraction equation, there are two methods we can utilize, one method is associated with the borrowing/regrouping values, the other method, which was written by me, is associated with carry-over values. For dealing with infinity numbers in a subtraction equation, I chose to utilize my method, which utilizes the carry-over values.

Similar to an addition equation, if we were to process the sub-equation of the digits from both numbers starting from left to right, we would not have an “Infinity Unchanged” value until we get a result value that when applying a carry-over value to will not modify any previous result value. One we get this value, any previous result value is the “Infinity Unchanged” value. In an addition formula, a value that is when applying a carry-over value to that would not modify any previous result value are anything but the maximum value that the digits set can hold. Opposite to that, in a subtraction equation, that value is anything but the lowest value that the digits set can hold. For example of when we are processing the subtraction equation at the rate of one digit at a time, then anything that is not the zero digit will not modify the previous result value even when applying a carry-over value to. This is because in my equation, bases on whether if the first number is the larger or the smaller number then the carry-over value would either be produced based on whether if the result value is a negative or a positive value. Thus, when speaking of a value that neither negative nor positive and is also the crossing point of being a negative or a positive value then in our numbering system, the smallest value that the digit set can hold is always that value, which is the zero digit. For example, if we were to have a zero result value for an equation of a current sets of digits and the next digits set that we were to process after this digits set has a carry-over value then we would need to apply that future carry-over value to the result value of the current equation, and because of that, the result value of the current equation would produce a carry-over value and that value would then need to be applied to the result value of the previous equation. We also have to remember that, this circumstance describing above is for when we are processing the digits from left to right, and the property of the carry-over value is that the carry-over values are always to be applied to the digits set that are to the left of where the carry-over value was produced.

In conclusion, the “Infinity Unchanged” value of an infinity subtraction equation of when we are assuming that we are processing the numbers from left to right are all the result values of the previous equations of the equation of the current digits set, and only when the current result value is not the smallest value that the digits set can hold.

**Multiplication and Infinity Unchanged for Infinity Post-Assumption:**

When it comes to the “Infinity Unchanged” value for a multiplication equation of infinity numbers that associated with “Infinity Post-Assumption”, I would first illustrate an example before going into describing the properties of “Infinity Unchanged” values of an infinity multiplication equation.

In this example of a multiplication equation of two infinity numbers, we are assuming that we are reading two numbers that are infinite in length and we are processing the equation starting from right to left of the numbers. For this example, we are applying the multiplication equation to the numbers at the rate of one digit at a time. Although in this demonstration, I stopped at the fifth digit, nevertheless, in principle, this can goes on indefinitely. In the example, A would be the first number and B would be the second number. To simplify the explanation, I would only apply one possibility to this case, and that possibility is both A and B are positive numbers.

1. For the first digit from A and B, we got a 9 for A and a 3 for B. The equation and the answer would look like the below.

9 * 3 = 27

At this instance in the equation, the “Infinity Unchanged” value is: “7”.

2. After the first digit of A and B, we got a 2 for A and a 8 for B as the second digits. A would now be 29 and B would be 83.

29 * 83 = 2407

From the result value of this instance in the equation, the “Infinity Unchanged” value is: “07”.

3. We then got a 5 for A and a 7 for B as the third digits. A would now be 529 and B would be 783.

529 * 783 = 414207

From the result of 414207, The “Infinity Unchanged” value would now be: “207”.

4. When it comes to the fourth digit of both numbers, we got a 8 for A and a 1 for B. A would now be 8529 and B would be 1783.

8529 * 1783 = 15207207

For now, the “Infinity Unchanged” value is “7207”.

5. For the final digit of this example, we got a 2 for A and a 9 for B. A would now be 28529 and B would be 91783.

28529 * 91783 = 2618477207

At this final state of the example, the “Infinity Unchanged” value is: “77207”.

If we were to process the multiplication equation of the numbers infinitely and the digits in the numbers continue to grow indefinitely, the total amount of digits in the “Infinity Unchanged” value will grow. Nevertheless, the digits that already contained by the “Infinity Unchanged”‘s value of the fifth step from the example above would eternally be the same while the “Infinity Unchanged”‘s value expand in the amount of digit.

To understand the reason of why the “State of Infinity Result Value” of a multiplication equation of infinity numbers produces “Infinity Unchanged” values, we should first examine the property of a multiplication equation. Assuming that we are multiplying all the digit from the first number, which in this case is number A, to all the digit in the second number, which in this case is number B, and at the rate of one digit at a time. During the beginning, after we had multiplied all the digit of number A to the first digit of number B, we would have what can be classified as a main temporary result value. For every time after, each time we completely multiplied all the digits from number A to another digit of number B, the equation would produce another temporary result value. All the subsequence temporary result value after the main temporary result would then be added to the main temporary result value bases on their order. The temporary result values can all be added together in one time and that time is when the equation does not produce anymore temporary result value or each subsequence temporary result values can be added to the main temporary result value right after being created.

In my opinion, there are two methods for explaining of how the temporary result values of a multiplication equation are added together. For the first interpretation, in a multiplication equation of when we are processing the digits from right to left, the digits of the subsequent temporary result values are placed below the digits of the main temporary result value, then we would combine the digit value of the temporary result values together. For the placement position, bases on the position of the main temporary result value, each time when we are placing a temporary result value below the main temporary result value, the entire string of digits of the temporary result value would move over to the left by one digit, and each time after, one more digit than the previous time. Also, we always have to place the temporary result value in the order of they are being created. In short, what was created first would be placed first and what was created second would be placed second and so forth.

In another interpretation, I would say that we would place an amount of the digit zero to the end of each subsequence temporary result value, and all the subsequent temporary result values would then be added to the main temporary result value. The amount of the digit zero start with one digit zero when the first subsequence temporary result value is created and would be placed to the end of the temporary result value at that instance. Thereafter, each time when a new temporary result value is created, the amount of the digit zero would increase by one more digit zero and would be placed right at that instance and at the end of the temporary result value.

The example below is the illustration of a multiplication equation for when we are processing the equation from the first digits of the right to the last digits of the left. Although, I wrote two methods of interpretation for adding the temporary result values together, in our daily explanation we would most likely stick to an explanation that similar to the first interpretation that I made from above. Therefore, I only illustrated an example that is associated with the first method of interpretation.

nnn *nnn ------ nnn nnn nnn ---------- nnnnn

With the example from above in context, the “Infinity Unchanged” value will always grow by one digit for an infinity multiplication equation of when we are processing the equation at the rate of one digit at a time, and of when the equation processing the digits in the numbers starting from the first digit on the right toward the last digit on the left. It does not matter how long the final answer is going to be, after multiplying all the digits in the first number to the first digit in the second number, the “Infinity Unchanged” value will be the rightmost digit of the current answer. When we moved onto the next digit in number B, the second rightmost digit in the current answer’s value would be added to the left side of the “Infinity Unchanged” value.

If we were to add more digits to the beginning of the numbers then all the digits in number A would be multiplied to the new digits in number B, and the new digit in number A would be multiplied to all the digit in number B except for the newest one. The new values from the multiplication process of the new digit from number A would always be placed at the beginning or the left side of the current temporary result values and would be placed in their correct position. The total value of the entire equation will almost always change when a new digit is added to both numbers. Nevertheless, we know one thing is for sure, and that is when a new digit is added to both numbers, our “Infinity Unchanged” value will increase by one digit. This can goes on infinitely. Nonetheless, we do not have to have any concern in regard to any carry-over value when it comes to the “Infinity Unchanged” value for this type of equation. This is because the carry-over values from the equation would always be added to the left side of the result/temporary values, and therefore, would not affect the digits/values that already became the “Infinity Unchanged” value.

**Multiplication and Infinity Unchanged for Infinity Pre-Assumption:**

The “Infinity Unchanged” value does also occur in a multiplication equation of infinity numbers of when we are assuming that we are reading the digits in the infinity numbers starting with the digits from the leftmost of the numbers. By knowing the properties of a multiplication equation of when the equation started with the rightmost digit of the numbers, we can apply the reversal on the properties to understand what procedures have to be made for a multiplication equation of when the equation started with the leftmost digit of the numbers. When the equation started from the leftmost digits, there is a large difference in the “Infinity Unchanged” value’s property. Since the carry-over value would always be added to an equation’s result value that is on the next left side of where the carry-over value was produced, the “Infinity Unchanged” value will not occur until the “State of Infinity Result Value” offer values that are safe from being modified by any future carry-over values. The example below will demonstrate a multiplication equation of when the equation started with the leftmost digit.

789 592 ------ 3945 7101 1578 ------ 467088 124 122 ----- 124 248 248 ----- 15128 124 129 ----- 124 248 1116 ----- 15996

From the example above, for working in reversal where are are multiplying digits starting from the front of the numbers at the rate of one digit at time, we are extending the answer string for each time we multiply all the digits from the first number to the second number by one digit toward the right side, and only one digit is the amount of digit that we can extend the answer string by. To extend the answer string by one digit, we would move the current temporary answer string over to the right by one digit if it needed to be.

With the properties from above in perspective, it may seem to be true that after we moved to the third set of digits in the numbers, the multiplication equation would always start producing an “Infinity Unchanged” value. Nevertheless, due to the property of the carry-over value, obtaining the “Infinity Unchanged” value for a multiplication equation would be a lot more complicated of when we are processing the equation from left to right of the numbers. This example below will demonstrate the complicatedness that associate with “Infinity Unchanged” values and “Infinity Pre-Assumption” in a multiplication equation of infinity numbers.

919 109 ------ 919 0 8271 ------ 100171

In the example from above, the example demonstrates that even at the third digit set, the equation still does not produce an “Infinity Unchanged” value. The exact solution of how we can obtain an “Infinity Unchanged” value for this type of equation is to understand of how to continually multiply the numbers together in circumstances of when we are continually adding additional digits to the right side of the numbers without have to multiply all the digits together each time we added a new digit to both numbers.

Before going into when an infinity multiplication equation produces an “Infinity Unchanged” value, we should first explore how can we keep on processing the equation as more digits are being added to the numbers on the right side of the numbers without having to restart the equation from the beginning. Let first look at an example before going into the explanation. In the example below, we are processing the equation from left to right of the numbers and digits are adding to the right side of the numbers.

Example 1: (3....) * (3....) (3 x 3) (35 * 38) (358 * 389) (3581 * 3892) (35811 * 38925) 3 35 358 3581 35811 3 38 389 3892 38925 -- ---- ------ -------- ---------- 9 -----> 9 -> 1330 -> 139262 -> 13937252 15 - 304 - 389 - 3892 280 - 3222 - 7162 - 179055 ---- - ------ - -------- - ---------- 1330 ----- 139262 ----- 13937252 ----- 1393943175 Answer: 35811 * 38925 = 1,393,943,175

Example 2: (9....) * (3....) (9 * 3) (93 * 35) (935 * 358) (9351 * 3581) (93517 * 35819) 9 93 935 9351 93517 3 35 358 3581 35819 -- ---- ------ -------- ---------- 27 ------> 27 ---> 3255 -> 334730 -> 33485931 9 - 175 - 358 - 25067 465 - 7480 - 9351 - 841653 ---- - ------ - -------- - ----------- 3255 ----- 334730 ----- 33485931 ----- 3349685423 Answer: 93517 * 35819 = 3,349,685,423

With the example above in context, for a simplify purpose, I defined A as the first number and B as the second number. A reminder to the example is that we are processing the multiplication equation from left to right of numbers, and we are adding a digit to both numbers after each time we obtained a result value for the equation. This would be similar to processing a multiplication equation for numbers that are very very large or infinite in length that we can never read all the digits in one single time. The equation from the example can go on indefinitely, nevertheless, the example only demonstrates up to the fifth digit.

From the example, every time there is a new digit that is added to the right of both numbers, we would first multiply the new digit in number A to all but the new digit in number B. The result from this procedure is then added to the result value from the previous equation where we had not added the new digit yet. When adding this result value to the previous result value, we would extend the length of the previous result value to the right by one digit and only by one digit. To be able to do that we would place the new result value under the previous value with the rightmost digit of this new result value to be placed one digit to the right of the rightmost digit of the previous result value. This space would always be an empty space. We can add this two result values together or wait until completing the next procedures.

After multiplying the newest digit in number A to all but the newest digit in number B, we would then multiply all the digit in number A to the newest digit in number B. If we had not added the two result values from the previous procedure together yet, we would place the result value from this procedure down below the two result values of the previous procedure, and with the rightmost digit of this result value being placed one digit to the right of the rightmost digit of the most right result value from the previous procedure. This space would never have any digit. We would then add the three values together. If we had already added the two result values from the previous procedure together, then we simply add this result value to the result value of the previous procedure, and extending the previous result value by one digit to the right by placing this result value under the previous result value and with the rightmost digit of this result value being placed one digit to the right of the rightmost digit of the result value from the previous procedure.

To be able to surely classified when we can surely obtain an “Infinity Unchanged” value from a left to right infinity multiplication equation, we should first inspect some properties from an ordinary multiplication equation and some properties from the above examples. In a multiplication equation when we are multiplying 1 digit to 1 digit, the maximum length the result value can be is 2 digits, and the minimum length the result value can be is 1 digit. For an example, 1 x 1, would produce an answer that is one digit in length, and 9 x 9 would produce a result value that is 2 digits in length. When it comes to more than one digit, if we multiply 5 digits to 5 digits, the maximum length the result value can be is 10 digits, and the minimum length the result value can be is 9 digits. For example, 10000 x 10000, would produce a result value that is 9 digits in length, and 99999 x 99999, would produce a result value that is 10 digits in length. Thus, we can say that the length of the result value of an equation of when two numbers multiply to each other at minimum is the total length of that two numbers minus one, and at maximum would always be the total length of the two numbers.

After inspecting the length property of a multiplication equation, the next thing we should inspect are the properties of multiplying an unknown or infinite length numbers starting from left to right by putting the procedures at the fifth digit from the above examples into context.

Example 1 Example 2 (35811 * 38925) (93517 * 35819) 35811 93517 38925 35819 ---------- ---------- 13937252 33485931 3892 25067 179055 841653 ---------- ----------- 1393943175 3349685423

To be able to find the “Infinity Unchanged” value for an infinity multiplication equation that started from left to right, we must evaluate the general outcome of the nearest future of the equation to find a location within the current “State of Infinity Result Value” that contain a value that does not alter any value before itself even when being modified by a carry-over value of the future. This location, I defined as “the location for calculating a safe value”. All values before “the location for calculating a safe value” can be an “Infinity Unchanged” value if the value within “the location for calculating a safe value” can’t modify any value before itself even if itself is being modified by a future carry-over value. To be able to find “the location for calculating a safe value”, we would first need to understand in possibility and in maximum, how many digits from the current “State of Infinity Result Value” can be affected by the future result value of when a new digit is being added to both numbers.

When looking at the examples, we know that every time we add a new digit to both numbers, we would multiply the newest digit in the first number to all but one digit in the second number. In length, the result value from this procedure at maximum can be the length of the second number. Nonetheless, in length and at maximum, if our equation already had a “State of Infinity Result Value” then the amount of digit in the “State of Infinity Result Value” that is going to be directly affected by this procedure’s result value of when adding the two result values together would be the length of the second number minus one digit. This is because the placement of this procedure’s result value would always be one placement over to the right of the rightmost digit in the “State of Infinity Result Value”.

For the second procedure of when a new digit is being added to both numbers, we would have to multiply all the digit in the first number to the newest digit in the second number. The length of the result value from this procedure would be the length of the second number plus one digit. However, when it comes to how many digits in the “State of Infinity Result Value” that is going to be directly affected by this procedure’s result value would be one digit less than the length of this procedure’s result value. This can also be said that this procedure result’s value can directly modify an amount of digit within the “State of Infinity Result Value” that is equal to the length of the second number.

Now, when I say directly, it is because I do not take into account the digits that could be modified as the result of when the procedures are being executed. This is because with the right combination of digits in the “State of Infinity Result Value”, all the digits within the “State of Infinity Result Value” could be modified as the result of executing the two procedures of when a new digit is added to both numbers. For this event to occur, the “State of Infinity Result Value” must contain the right combination of digits, and what modified the entire value of the “State of Infinity Result Value” is a carry-over value that produced by the current equation.

From the explanation, when combining the two procedures’ result values together with the “State of Infinity Result Value”, we know that the first procedure’s result value could modify an amount of digits within the “State of Infinity Result Value” that is one length less than the length of the second number, and the second procedure’s result value could modify an amount of digits within the “State of Infinity Result Value” that is equal to the length of the second number. A key point here is that when applying the infinity multiplication equation from left to right, we would always count from right to left the amount of digits within the “State of Infinity Result Value” that is going to be directly affected or affected by the current or future procedures’ result values.

Another important point in this equation is when combining the two result values of the two procedures to the “State of Infinity Result Value”, there would be three sets of numbers that would be added together. At any part of the “State of Infinity Result Value” that is directly affected by the addition procedure, there is a chance that the carry-over value can be a value of two. The property of a carry-over value that can be a two in value can go on and affect one more space than the length of all the digits that are directly affected by the equation. However, the carry-over value can never be more than a two in value when there are only three sets of digits that are being added together. For example, 9 + 9 + 9, would be 27. With the previous example in context, in an addition equation of when there are still more digits to be processed by the equation, the 7 would be the result value for the current position and the 2 would be the carry-over value that would carry-over to the next procedure of the next position to the left of the current position.

In summary of the explanation, when combining new result values to the “State Of Infinity Result Values”, at maximum, the amount of digits within the “State Of Infinity Result Value” that is going to be affected by an equation that involves adding three set of numbers together is the length of the second number minus one digit. After that and if the third set of number is long enough, the next digit in the “State Of Infinity Result Value” will be affected by an addition equation that involves adding two sets of numbers together. In this procedure of when there are only two numbers left in the addition procedure because of the third set of number is long enough, the result value from the procedure can have a carry-over value of two if there was a carry-over value of two from the previous procedure of when there were three sets of numbers in the equation. This is because if there is a carry-over value of two from the previous procedure then that carry-over value of two when added to the maximum result value that can be produced by adding two digits together can potentially produce a carry-over value of two. For example, 9 + 9 = 18, and when adding 18 to 2, we would get 20 as a result value. From this explanation, we know that it can be complicated if we were to defined “the location for calculating a safe value” is the next location right after of the last digit within the “State Of Infinity Result Value” that is going to be directly affected by the future procedure’s result value of when a new digit is added to both numbers. This is simply because of the value of that location has a possibility of absorbing a carry-over value of two. It is possible to define that location as “the location for calculating a safe value”. Nonetheless, it would be simpler to just move over to the left one more location from the location of where the last digit in the “State of Infinity Result Value” that would be affected by the nearest future procedure. There is a high potential that we would obtain the “Infinity Unchanged” value one step behind of when the value was formed. Nonetheless, with this method, our procedures are much simpler. By having one location later, we only have to evaluate if the digit within that location is the digit 9 or not. Otherwise, we would have to evaluate both, if the location contained the digit 9/8 or not. However, this can come down the matter of taste in simplicity, nevertheless, for this article’s explanation, I would use the simpler method.

With the explanation above in perspective, when exploring the “Infinity Unchanged” value that is associated with an infinity multiplication equation from left to right, there can be many methods for finding the “Infinity Unchanged” value that may be available or discoverable in the near future. Nonetheless, I would only introduce the method that I am most familiar with and is one of the simplest methods. The first property of this method is we would evaluate the condition of when in the equation we can start to evaluate the result value to search for whether if there is an “Infinity Unchanged” value.

In the beginning of a from left to right multiplication equation of two infinite numbers and we are considering that the equation is being applied at the rate of one digit at a time, we would first have a single digit in both numbers. The maximum amount of digits that can be produced by the result value of this procedure has the potential to be two digits. Nonetheless, in my opinion, instead of using the maximum amount, we should use the minimum amount, and the minimum amount is one digit.

When foresee into the nearest future of the equation, we would have a digit added to the right side of both numbers. When adding a new digit to the numbers, in principle, there is a potential that the procedures which we have to apply to the future equation have the potential to directly modify two digits in our current result value. Nonetheless, in reality, there is an exception in this case. Since we only have one digit in our current result value, the future equation would always only to directly be affected to one digit in our current result value. Only one digit from the current result value can directly be affected by the future equation, nevertheless, there is a potential that after being affected by the future equation, besides the two digits that would grow on the right of the only digit in the current result value, another digit can grow to the left due to the potential of a carry-over value. To put this clearly in a perspective, we should first explore a couple of examples. In the examples below, I took out the first digit procedure part of the equation to shorten the examples, nevertheless, they are not different from the far above examples of this section.

(39 * 39) (19 * 49) (19 * 99) 39 19 19 39 49 99 ---- --- ---- 9 4 9 <--- Result From Previous Equation 27 36 81 351 171 171 ---- --- ---- 1521 931 1881

From the just above explanation and examples, we know that we can't calculate the "Infinity Unchanged" right at the start of the equation. Now, let us move onto when there is the second digit in the numbers. At this point in time, at a minimum, the result value from the equation can be two digits in length. With the current result value that at minimum is two digits in length, we would evaluate the nearest future of the equation of when there is another digit that is added to both numbers. At this nearest future, both our numbers will be three digits in length, and therefore, the procedures of the future equation have the potential of directly affecting three digits in our current result value. Thus, we still can't calculate the "Infinity Unchanged" value at this instance in the equation.

After the instance of the second digit, when it comes to the result value of when both infinity numbers contained the third digit, the result value of the equation as of now can be at a minimum of five digits in length. When evaluating the equation to the nearest future of when there is another digit that would be added to both numbers, and at that moment, both the numbers will be four digits in length. At that point in time, the amount of digit from the current "State of Infinity Result Value" that can be affected by the future equation is four digits. With this, it seems that we can start to evaluate the "State Of Infinity Result Value" to search for an "Infinity Unchanged" value at this point in time. This is due to the reason that we would have at least five digits in the "State Of Infinity Result Value", and at a maximum, only four of them can directly be affected by the procedures of the future equation. Nonetheless, there is one digit that has a potential to be affected by a carry-over value that at a maximum can be a value of two. Thus, in my opinion, it is better that we do not calculate the "Infinity Unchanged" value at this instance in the equation. Therefore, we would just move onto the equation of when both numbers have a fourth digit.

At the time of when both the infinity numbers have the fourth digit, the result value for the equation at a minimum can be seven digits in length. When moving onto evaluating of how many digits from the current result value that would be affected by the procedures of the nearest future equation of when a new digit is being added to both numbers, we know that at most there are going to be five digits that would be affected by the result values from the procedures of the future equation. Also, one digit can be affected by a carry-over value of two. From that, we only have one digit left to spare, and that is the seventh digits in the result value. The seventh digit from the current result value is a digit that would never be affected by a carry-over value of two. That seventh digit location is "the location for calculating a safe value". If this location if affected by a carry-over value then the carry-over value that affecting this location can only be a value of one. Thus, if the digit in this location is not a nine digit and if we have an eighth digit in the current result value then that the eighth digit is the "Infinity Unchanged" value.

From the above paragraph, when we are looking at what could happen when both of our infinity numbers have a fourth digit, we can understand the properties of "the location for calculating a safe value". To get "the location for calculating a safe value" in the current "State Of Infinity Result Value", we would count from right to left of the current "State Of Infinity Result Value" an amount of digits that is equal to two plus the length of the second numbers of the nearest future of when another digit is going to be added to both numbers. If the value in this location is a value that when altered by a carry-over value of one does not produce a carry-over, then any value on the left of this location is the "Infinity Unchanged" value. In a case of a multiplication equation where the equation is being applied at the rate of one digit at a time, then any value that is not a digit 9 is a safe value, and when altered by a carry-over value of one, will not produce any carry-over value.

In a conclusion, in a left to right multiplication equation of infinity numbers, at the fourth digit and after, we can evaluate if there is an "Infinity Unchanged" value within the "State Of Infinity Result Value" by evaluating a value that is in the location that from right to left of the "State Of Infinity Result Value" that is equal to 2 plus the length of the second numbers in the nearest future equation. If the value within this location does not produce a carry-over value in the event where the value is being altered by a carry-over value of one then any value to the left of this location, if there is, is the "State Of Infinity Result Value".

# Conclusion Of Formula 1

For a conclusion, when exploring deeper into how we would or may calculate numbers that are very large in length or are infinite in length, we can see that there are many assumptions that we have to make to get what could be the result value for the entire equation. For unknown length numbers, we may reach that ending just one digit away or we may not. For numbers that are infinite in length, we would never reach that ending. Nonetheless, our assumption would always have to be made. Thus, it is why I defined the first part of my formula as infC = infA, or "Infinity Calculation" equal to "Infinity Assumption".

While being inside an equation of numbers that are infinite in length or of an unknown length, we would constantly produce result values that would constantly change as new digits are being added to the numbers. Thus, our result value would never be the same until we reach the ending of the equation. That is if there is an ending to the equation. Within that ever altering result value, in some type of equation(addition, subtraction, and multiplication), we would have some part from the result value that would never change even when new digits are being added to both numbers. That unchanged value would also expand in length as our numbers grow to be larger. Nonetheless, as we are continually processing the equation for the numbers, the totality of the result value would always alter. Thus, in my opinion, it is safe to piece up the formula and say that, while calculating a result value for infinity numbers, we would always have many assumptions to be made to be able to actually calculate what may be the result value for the entire equation in the event that we do reach an ending. Additionally, while making many assumptions and processing the equation at the same time, the result value from the equation of the part of the numbers that is seeable by the equation and by our assumption would always alter. Thus, I concluded that, infC = infA = infAL, or "Infinity Calculation equal Infinity Assumption equal Infinity Alteration".

For a similar comparison, I would compare the equation of calculating infinity numbers as a similar event of an equation of living through time. Time could just be infinite in length, or time could also just be of an unknown length. We may never know this, and it is because we have not reached the end of time. Does time have an ending, or is time an endlessly repeating loop, or does time flow in a straight line, a straight line that will never end? We may never know. Nonetheless, we are living our daily life and experiencing all events that occur within time, time that may never end or may end tomorrow. When it comes to interaction, we interact with countless people and objects in our daily life. Each interaction can be considered as a mathematical equation if we want to consider it to be. How much distances our eyes have to move to see the sky, or how many steps we have taken to reach where we wanted to arrive to, or the distances between us and what our eyes see, and much more are all processed by our brain. We do not feel that it is a mathematical equation simply because our brain already processed everything for us and let us perceive all that around us into images, feelings, and sounds. Besides that, each of our decision may affect the future of another person or object that is/are around us. Therefore, in my opinion, it seems like we are living inside an infinite string of number that may never run out of digits.

When it comes to assuming life, we would always assume that there is a tomorrow, although if there is a tomorrow or not, no one knows for sure, and it is because no one knows when time would collapse or if time would flow endlessly. Nevertheless, whether if there is a tomorrow or not, we would always want to assume that there will be a tomorrow. With this, we would always thrive our life in happiness and thrive our achievement to the maximum extent. We would also want to assume the best even in a situation where the probability of the worst scenario is as large as ever. This is to keep us happy and give us the ability to be able to thrive forward, nevertheless, that doesn't mean we wouldn't calculate for what if it is the worst scenario that going to happen. From this comparison, doesn't it feel that living through time is being within a mathematical infinity calculation, like the one that was described in this article? For me it is.

**--- This is the end of Kevin's Infinity Formula - Part 1 ---**

**--- The below is a preview of Part 2 and will be removed one Part 2 is released. ---**

#### --- Formula 2: Infinity Numbers With A Single Constant Digit ---

**The second formula: "infN e infN = infP".**

When we are dealing with numbers that only contain a single digit and assuming that is the only type of number that we are dealing with in our equation, we can obtain the "Infinity Result Value" on the pattern of result value from the same type of mathematical equation that apply to the numbers in certain length as if the digits were not infinity.

This is because, in a majority of mathematical events, where you are applying a mathematical equation on a number that is in a certain length and only contains one type of digit to another number that has the exact same property, there would be repeating pattern once the number grows to a certain length. For example, if we were multiplying a nine to a nine, we would get eighty-one. Now, if we add another nine to both numbers, we would get 9801. After, if we add another nine to both numbers, what we get is 998001. As from the result value of the previous, we can see that there is a repeating pattern, but to be sure we would add two more nine to both strings of numbers. Our equation would now look like 99999 * 99999, and the result value would be 9999800001. With this result value, we can see one pattern. Doesn't matter how many nine both numbers can contain, as long as they are both equal in length, we would always have an unknown amount of nine, one digit eight, an unknown amount of zero and a single one. To write this as a equation result value, I would write this as "∞9 x ∞9 = [∞9][8][∞0][1].".

Not all single type of digit number equate to another single type of digit number would produce a completely unchanged repeating pattern as a result value. Nevertheless, they do, however, produce some pattern that would never change after a certain length. I have two set of words that describe for all my formula for a value that would never change in a mathematical equation that deals with infinity numbers and they are "Infinity Unchanged" or "Eternal Unchanged". What would contain in the result value if there were number would be an unchanged value, an infinity alteration value, and an unchanging pattern.

As for comparing this to time, on a smaller scale, I would use my birthday as an example. If I was to be alive for an amount of time and every year I would always have a birthday on the same day, we could say that I have an infinity amount of birthday. When we are treating the event of my birthday as a mathematical equation, there would be an unchanged pattern and an infinity alteration pattern. The unchanged pattern would be my birthday will occur on the same day every year. Even if the timing can be constantly the same throughout the years, the changing pattern could be how many people will attend my birthday or what type of food I will order. How early I need to prepare my birthday or how long it would take for me to cook or order the food or how long it would take for me to invite everyone to attend my birthday are timing events that could change even if my birthday was to start at the exact timing every year. the amount of birthday. When we are treating the event of my birthday as a mathematical equation, there would be an unchanged pattern and an infinity alteration pattern. The unchanged pattern would be my birthday will occur on the same day every year. Even if the timing can be constantly the same throughout the years, the changing pattern could be how many people will attend my birthday or what type of food I will order. How early I need to prepare my birthday or how long it would take for me to cook or order the food or how long it would take for me to invite everyone to attend my birthday are timing events that could change even if my birthday was to start at the exact timing every year.

On a larger scale, we can use our rotation between earth and the sun and an example. Let assume that our planet will rotate around the sun the exact same amount of times every year, and that cycle will continue infinitely. If we were to treat the event as a mathematical equation, our constant value would be the amount of time and rotation the earth rotates around the sun in one single year. The distance between the earth and the sun would be a constant every single year, this is because if the distance changes our rotation time would change due to the force of gravity. Nevertheless, there are other changing events that would occur. How much sunlight the surface of the earth would receive may not be the same, this is due to how much sunlight the core of the sun produce may change throughout time. How much or many solar storms the surface of the earth would receive could also change throughout time. These events would still be considered as time events.

In a perspective, I describe this formula as a formula for dealing with "Infinity Numbers With A Single Constant Digit".

**Please do not republish beyond the noted red text in the beginning of the article without author's consent, Thank you for understanding.**

This post was written by Kevin and was first post @ http://kevinhng86.iblog.website.

Original Post Name: "Kevin’s Infinity Formula".

Original Post Link: https://kevinhng86.iblog.website/2017/04/28/kevins-infinity-formula/.

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