As far as describing it in an intelligent way, just say that infinity is not a number because infinity is a meta word not in the set but used to describe the set. Just as the words "unbounded" and "non-empty" are (usually) not considered as numbers, infinity is (often) not considered as a number.

Is infinity a number or not?

Infinity is not a number. Instead, it's a kind of number. You need infinite numbers to talk about and compare amounts that are unending, but some unending amounts—some infinities—are literally bigger than others. Let's visit some of them and count past them.

Why infinity is not a real number?

Infinity is a "real" and useful concept. However, infinity is not a member of the mathematically defined set of "real numbers" and, therefore, it is not a number on the real number line. ... One of the most common definitions to learn then is that the real numbers are the set of Dedekind cuts of the rational numbers.