Dear uncle bataleur, or anyone else who knows the answer...

[babysaxon]

If infinity is bigger than any numbers, what happens when we try to count up to it?

(Ed. : I'm not kidding, she really did ask this over dinner just now!!)

Comments

[bateleur]

It's a very good question!

Mostly the answer is the same as what happens if you count up to any really, really big number: you give up before you get there.

The only time the difference between infinity and other very big numbers actually matters is if you use it in sums. That can get complicated. At that point you can do one of two things:

1) Do what most people do and guess at the answer (and maybe get it wrong).

2) Substitute some algebraic variable into the places where you have infinity in your expression (let's say "X", because mathematicians love that letter due to the way it reminds them of pirates). Then try to deduce whether the resulting function of X converges as X tends to infinity. Surprisingly often you can work this out by just writing down a few terms, but don't pick "1,2,3..." because some common functions are very irregular for small numbers, go for "1,10,100,1000...".

That's enough for now. When you're older you'll learn some techniques which will enable you to be a bit more exact about what you mean by "convergent" and be a bit more systematic about proving convergence. For now, "Mummy, it's convergent if I say it is!" will do fine and is in any case broadly equivalent to numerous arguments used by my lecturers.

[cuthbertcross]

Useful stuff (she was very happy to hear you thought it was a good question!)