Infinity

Infinity

- I am going to use sympy lib to represnt all math here



main math

What is inifity?

explain the unexplainable

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First of all, I think that it is one of the most beautiful concepts in math. It can build mountains and define world smaller than microns all together.
And to the more practical things:
Its sgin is:
But what does that mean?
You have multiple ways to look at it, but the main ways that are used the most. and are the most practical, I think are:
1.
You can look at it as a process, some kind of a model for an unending process.
If you want to define a process that never stops - define it with infinity.


2.
You can look at it as a number.
The biggest number exist.


But what does that mean?
Lets try to combine those ways. To get the bigger picture

Example1
Lets try to find the biggest number exists.
Obviously, we cannot think of one... No matter how hard we search for it, no matter what number we choose,
we can find a number that is bigger than it if we only do the simple task of adding 1...
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So instead of finding the biggest number exist, lets define the process of finding it.
You encountered a number? take a number that is bigger than it.
And now define some aspect of infinity.
The definition of this so called "BIGGEST" number, defines in it some process.

If we define anything for this "number" called inifinity, it means that no matter how far we got he definition still occurs.
That's why we don't need this exact number, like 1,2,3, and that's how we treat inifinity as some kind of a "process" too.

For example something that happens:
o . When we get close to a number:
x → 1
x → 0
2. When we try to get infinity:
x → ∞

All of them are some kind of inifity.
If you are approaching a number, just substract from the number the number we are approaching to and multiply by (-1), and you get approaching to zero.
For example - approaching 4 from the "right" side means:
... 4.1, 4.09, 4.08, 4.07, 4.06 ...... 4.0000000000001 ....
And if you substract the fixed part - 4, you get:
... 0.1, 0.09, 0.08, 0.07, 0.06 ....... 0.0000000000001 ....

If you approach from the "left" side, multiple everything by (-1) and you ge approaching to zero from the "left" side
... 3.9, 3.91, 3.92, 3.93, 3.94 ....... 3.9999999999991 ....
Substract -4, multiple by (-1):
... -0.1, -0.9, -0.8, -0.7, -0.6 ....... -0.000000000001 ...

Approaching to zero can be looked at a fixed number devided by a number that id getting bigger:
1, 0.1, 0.01, 0.001 .... 0.0000000000000001 ...
If you look at the denominator of these numbers you will see that its growing.
1, 10, 100, 1000 ... 10000000000000000 ...
It will happen with every sequence of numbers that is getting close to zero - If you have a fixed value in the numeratorm the denominator will grow.
So again, the process that changes the number is the unending growth of the denominator - approaching infinity.
In the end of all of this, everything revolves around what inifinity represents.


And before leaving, this is how infinity realy looks like




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