My children both learned about infinity at around four to five years old (now 5 and 7). For both of them it was fairly straightforward; it came about with my eldest when he was talking to other kids at school about the biggest number. We talked about trillion, quadrillion, etc.; as they were at a Montessori, it was easy to understand these. Then we talked about googol, and googolplex. Then we talked about a few other numbers, like Graham's number, and the idea of other extremely large numbers.

Finally, we talked about infinity. Because we were talking in the context of very large numbers, the first thing we learned - before anything else - was that infinity is a concept, not a number. A way of thinking about extremely, impossibly large numbers, without actually naming one. This brought a little confusion, until we went through the thought exercise of: "What's the largest number. Okay, add one to it." But ultimately they got the idea of 'concept' pretty easily.

Now, at 5 (almost 6) and 7, they get some of the other ideas pretty easily - like 1/0 = infinity, infinty/n =infinity, but 0/infinity = undefined. Teaching infinity as a concept made it easy for them to understand these are basically just rules to follow, and that it's not the same as a number.

Of course, I had a lot of sympathy that week for the poor preschool teacher who had to deal with the arguments 'infinty is the biggest number' 'no, it's a concept, not a number' between my children and the other children...

My children both learned about infinity at around four to five years old (now 5 and 7). For both of them it was fairly straightforward; it came about with my eldest when he was talking to other kids at school about the biggest number. We talked about trillion, quadrillion, etc.; as they were at a Montessori, it was easy to understand these. Then we talked about googol, and googolplex. Then we talked about a few other numbers, like Graham's number, and the idea of other extremely large numbers.

Finally, we talked about infinity. Because we were talking in the context of very large numbers, the first thing we learned - before anything else - was that infinity is a concept, not a number. A way of thinking about extremely, impossibly large numbers, without actually naming one. This brought a little confusion, until we went through the thought exercise of: "What's the largest number. Okay, add one to it." But ultimately they got the idea of 'concept' pretty easily.

Now, at 5 (almost 6) and 7, they get some of the other ideas pretty easily - like 1/0 approaches infinity, infinty/n is infinity, but 0/0 = undefined. Teaching infinity as a concept made it easy for them to understand these are basically just rules to follow, and that it's not the same as a number.

Of course, I had a lot of sympathy that week for the poor preschool teacher who had to deal with the arguments 'infinty is the biggest number' 'no, it's a concept, not a number' between my children and the other children...