My son, also 6 yo, regularly talks about millions and billions and infinity. Obviously, large numbers have some attraction to children of this age.

I try to explain that infinity is not a number. Instead, infinity is an _order of magnitude_ which has its own algebraic rules. Plus, minus, divison and multiplication do not work the way children learn in elementary school when applied to with infinity.

My first explanation is that this has also an impact on how we use the words _infinity_ and _infinite_:

> Three meters. (works)

> *Infinity meters. (completely wrong)

> *Infinite meters. (sounds wrong)

> Infinite many meters. (works)


Another approach is that the concept of numbers does not work. Numbers grow. For every number, there is another number that is larger. The mathematical notation to this concept is $\forall n \in \mathbb{N}: \exists m \in \mathbb{N}: m > n$. If infinity was a number, than this statement would be false, because let $n=\infty$, then $\infty + m > \infty$ is false for all $m \in \mathbb{N}$. Surprisingly, children who already learnt addition upto, say, 100, understand this. They understand that 100 is not the end highest of all numbers, neither is 1000, neither is a million, and so on.