I was putting Alex and Kyra to bed tonight and Alex asked a deep mathematic question:
“Dad, how far is it from two to infinity?”
I pondered that for a moment (partially wondering where the heck it came from) and finally said, “Well, infinity is forever. So it’s forever from two to infinity.”
“But how big a number is infinity?”
“Infinity isn’t actually a number. It’s higher than all the other numbers.”
“How high do the numbers go?”
“They go forever. All the way to… err… infinity.”
Obviously I’d been trapped by my own argument. Infinity isn’t a number, but the numbers reach all the way to infinity. As I said my good-nights and turned out the light, I was left wondering how to explain the concept of infinity to a six-year-old. It’s not really something you’d expect until a calculus course…