TITLE: Is infinity a real number?
QUESTION [13 upvotes]: Is infinity a real number?
If not, why not?
I want some very good arguments. 
Thanks.
$$\rightarrow\leftarrow\Huge\Huge\Huge\boldsymbol\infty$$

REPLY [7 votes]: Infinity $(\infty)$ is not a real number, it is merely an abstract concept describing something that has no end. Boundless! We could 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 "$\infty$". For example:
$$\infty+1=\infty$$
Which says that infinity plus one is still equal to infinity, even
$$\infty+\infty=\infty$$
If something is already endless, you can add $1$ or any number you want and it will still be endless.
Infinity cannot be measured, even the universe itself cannot compete with infinity. Most things we know have an end, but infinity does not.