Infinity

While studying mathematics, we often come along to the special symbol named infinity, ∞.
But what is infinity ?

Infinity ...
	... it's not big ...
	... it's not huge ...
	... it's not tremendously large ...
	... it's not extremely humongously enormous ...
	... it's ...

Endless!

There are few facts about infinity.

1. Infinity has no end

Infinity is the idea of something that has no end.

In our world we don't have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity.

So don't think like that (it just hurts your brain!). Just think "endless", or "boundless".

If there is no reason something should stop, then it is infinite.

2. Infinity does not grow

Infinity is not "getting larger", it is already fully formed.

Sometimes people (including me) say it "goes on and on" which sounds like it is growing somehow. But infinity does not do anything, it just is.

3. Infinity is not a real number

Infinity is not a real number, it is an idea. An idea of something without an end.

Infinity cannot be measured.

Even these faraway galaxies can't compete with infinity.

Using Infinity

We can sometimes use infinity like it is a number, but infinity does not behave like a real number.

To help you understand, think "endless" whenever you see the infinity symbol "∞":

For example: ∞ + 1 = ∞

Which says that infinity plus one is still equal to infinity.

When something is already endless, we can add 1 and it is still endless.

The most important thing about infinity is that:

-∞ < x < ∞ Where x is a real number

Which is mathematical shorthand for
"negative infinity is less than any real number,
and infinity is greater than any real number"

Here are some properties of infinity:

Special Properties of Infinity
∞ + ∞ = ∞
-∞ + -∞ = -∞
∞ × ∞ = ∞
-∞ × -∞ = ∞
-∞ × ∞ = -∞
x + ∞ = ∞
x + (-∞) = -∞
x - ∞ = -∞
x - (-∞) = ∞
For x>0 :
x × ∞ = ∞
x × (-∞) = -∞
For x<0 :
x × ∞ = -∞
x × (-∞) = ∞

Conclusion

Infinity is a simple idea: "endless". Most things we know have an end, but infinity does not.

Reference: https://www.mathsisfun.com/numbers/infinity.html

~Chow Cheng Li