Is infinity a real number? Is infinity a real number?
If not, why not?
I want some very good arguments. 
Thanks.
$$\rightarrow\leftarrow\Huge\Huge\Huge\boldsymbol\infty$$
 A: No. If you look up the definition of the real numbers, you will not find any of its elements called "infinity".
However, the extended real numbers has two numbers called $+\infty$ and $-\infty$, which become the endpoints of the number line in the extended reals.
There are other structures that have an element or places named "infinity" that are similar but often different.
There are other situations where there are "infinite" objects, although we would never use the noun "infinity" to refer to them; e.g. the infinite cardinal numbers and ordinal numbers, or the unlimited hyperreal numbers.
A: 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.
A: Infinity isn't a real number by definition.
This definition is sensible because adding $\infty$ to $\mathbb{R}$ would break its field structure, and the fact that $\mathbb{R}$ is a field brings a lot of nice properties to real numbers
