Mathematics is the most exact science of all sciences – it is the perfect epitome of science. However, some semi-professional mathematicians have managed to introduce in the modern books of mathematics confusions which are causing problems with students when they try to understand mathematics. And there are three main issues in mathematics which need to be clarified:

- “IMAGINARY” NUMBERS
- INFINITY
- THE FUNDAMENTAL AXIOM OF MATHEMATICS.

By the way, especially because of the fundamental axiom of mathematics mentioned in part 3, this is the most important article in the history of mathematics. But let’s deal with the less important part first, which has to do with the so called “imaginary numbers”.

## 1: IMAGINARY NUMBERS

The so-called IMAGINARY NUMBERS are denoted with an “i” in mathematics. Whomever discovered them called them ‘imaginary’ because he thought that he was simply using a dirty trick to solve Quadratic Equations, without realizing that they really existed.

The question arises, “If they are not real, how come they always work?” As a matter of fact, let’s give examples of why the so called ‘imaginary’ numbers are just as real as the real numbers.

This ‘i’ (for ‘imaginary’) is found all over the equations of quantum mechanics which is the basis of modern physics. For example, the Schrodinger Equation has an ‘i’ in it:

Also, the Dirac Equation, has an “i” in it:

So, can you call physics imaginary, which are things which we can touch?

As a matter of fact, Paul Dirac predicted the existence of antimatter simply using this ‘i’ and guess what, today we know that antimatter does exist. It exists in small quantities in the observable universe, and it’s also being produced artificially in high energy accelerators in many labs around the world.

So, in fact, the so-called ‘imaginary’ numbers are real numbers in a perpendicular dimension, which can be a real physical hyper-dimension, like the 4^{th} dimension and 5^{th} dimension, as predicted by Einstein’s Theory, or all the way to the 10^{th} dimension as predicted by String Theory).

So, the ‘i’ is not imaginary at all. It works. How can you call something which always works ‘imaginary’. Equations which deal with electricity have the so called imaginary numbers, and you can try and touch electricity and see if it’s real or imaginary. However, it’s not the mission of this article to fix the books of mathematics, so we can still use the “i” in all the books of mathematics, but the correct way to call them would be to call them “invisible numbers” instead of “imaginary numbers”, because the so called imaginary numbers are real numbers but they are invisible numbers which exist in a perpendicular direction.

In the Quran, this is expressed by verses 69:38-39, which say, “I swear by what you see, and what you do not see”

## 2: INFINITY

In many well established books of mathematics, you can find the expression:

1+2+3+4+…=-1/12

What they are saying is that if we add all the numbers from 1 all the way to infinity, we will get -1/12.

This value can be reached through the Ramanujan Summation, or the Rieman Zeta Function Regularization, or Analytical Continuation, but in fact none of these methods are pure mathematics. When we use some of these methods, which deal with divergent series, or other things which have implied infinities in them, we are assuming that we can count all the way to infinity, surpass it, come back to zero, and then and only then we would get the value -1/12, for example. But, we already know that we can not count all the way to infinity, so by using these methods, we are assuming something which is not possible. Therefore, adding all the numbers all the way to infinity does not equal to -1/12.

Mathematics is the science of counting, and if you can not count to infinity, it means that Infinity is beyond mathematics. Infinity does not bend to the rules of mathematics, but it is mathematics which bends to the rules of Infinity.

And this can be indirectly implied from many verses in the Quran:

*[19:94] He has encompassed them, and has* **count***ed them one by one.*

*[72:28] This is to ascertain that they have delivered their Lord’s messages. He is fully aware of what they have. He has* **count***ed the numbers of all things.*

*[57:3] He is the* **Alpha***and the Omega. He is the Outermost and the Innermost. He is fully aware of all things.*

*[78:29] **We* **count***ed everything in a record.*

*[70:3] From GOD; Possessor of* **the highest***Height.*

*[40:15] Possessor of* **the highest***ranks, and Ruler of the whole dominion. He sends inspiration, bearing His commands, to whomever He chooses from among His servants, to warn about the Day of Summoning.*

*[2:15] GOD mocks them, and leads them on in their transgressions, blundering.*

And really all the crazy attempts to manipulate with Infinity emerge from the fact that mathematicians do not know, or take for granted the fundamental axiom of mathematics, which is explained below.

## 3: THE FUNDAMENTAL AXIOM OF MATHEMATICS

Now, let’s get introduced to the fundamental axiom of mathematics. It can be called “THE AXIOM OF EXCLUSIVE IDENTITY”. According to this axiom, each number has an exclusive identity. For example, number 2 is exclusively 2. 3 is exclusively 3. So,

There is no other 3 except for 3.

There is no other 4 except for 4.

There is no other 5 except for 5.

There is no other 6 except for 6.

There is no other 5000 except for 5000.

Even if we write these numbers in two places, the number which was written in one place and the one which were written in another place are still the same number. It’s not two different 3s for example, but only one number 3 exists. Number 3 is the same in the other side of the world, it’s even the same outside of this universe, at another time, in another place, it doesn’t matter, it’s the same 3. That’s why when we add 3 to 4 it always gives us 7, because it’s the same 3 and the same 4. So two different 3s do not exist. So 3 is exclusively 3. It’s not 4, it’s not 5, it’s not another 3, it’s the same 3. Likewise:

There is no other 4 except for 4.

There is no other 5 except for 5.

There is no other 6 except for 6.

There is no other 5000 except for 5000.

There is no other 1,000,000 except for 1,000,000.

And there is no other Infinity except for Infinity.

So, using the Axiom of Exclusive Identity we can reach the conclusion that:

**There is no other Infinity except for Infinity. **

And here is why this is important. It’s important because using this axiom, when we face the problems arising from Ramanujan Summations, for example, it will be very easy to understand. Here is an example:

Let’s say we try to add the numbers 1+2+3+4+5+…+∞, and this is known to be equal to ((∞+1)*∞)/2. However, once we see that the expression suggests that there will be 1 added ∞ (infinity), then we immediately recognize that it would be another infinity which would be bigger than the previous infinity, which would suggest that there are two infinities. However, this violates the fundamental axiom of mathematics, because according to it, there can be only one infinity. So, this means that the solution to this problem does not exist. So admitting that the fundamental axiom of mathematics supersedes the other rules of mathematics, leads us to the correct conclusion. However, had we applied the rules of mathematics even in cases where they violate the fundamental axiom of mathematics, then we could get the wrong results, while not being aware that we have crossed the boundaries of what mathematics can do. So, the solution to the expression 1+2+3+4+5+…+∞ is simply beyond mathematics.

**CONCLUSION:**

EVERYTHING is within the scientific scope of mathematics, except for Infinity.

And it is an axiom which extends all the way to INFINITY. This is how we express it in mathematical language, but in religious language, it is expressed in the Quran in many verses like:

*[57:3] He is the Alpha and the Omega. He is the Outermost and the Innermost. He is fully aware of all things.*

*[3:18] GOD bears witness that there is no god except He, and so do the angels and those who possess knowledge. Truthfully and equitably, He is the absolute god; there is no god but He, the Almighty, Most Wise.*