This happened a while ago. I kept meaning to blog it, mainly to economize on my telling it to relatives, but better late than never. My son Clark is 6. Here is our exchange:
Clark: Daddy why can’t there be a biggest number?
Bob: Because no matter how big a number is, there is always a bigger number.
Clark (puzzled): Why?
Bob: OK, let’s say a guy comes up to me and says, “Hey, I know the biggest number!” Then I would say, “Oh yeah, what is it?” And the guy would tell me, “It’s a billion billion.” But then I would just add 1 to it, and say, “A ha, a billion billion and 1 is a bigger number. So you made a mistake when you said you thought of the biggest number.”
Clark (after a pause): What guy are you talking about?
Bob: Just any guy. I’m saying, if anybody tries to think of the biggest number, I’ll always be able to do that trick–where I add 1 to it–so they can’t do it. They’ll always lose.
Clark: What if a girl asks you?
[I ran through the same thing with a girl asking me…]
Clark: OK I want to tell the story!
Bob: Sure go ahead.
Clark: So what if a guy came up to me and said, “Hey Clark, I know the biggest number! It’s 100 billion!” Then I would say, “No, 100 billion and 1 is bigger! You’re wrong!”
Bob: Right, good job. So he didn’t really think of the biggest number after all, did he?
Bob: And you can always do that.
Clark: OK let me tell it again with Sam [name possibly changed–a kid from his class].
Clark: So what if Sam came up to me and said, “Hey Clark, I know the biggest number. It’s 50 googol.” But I would say, “No Sam you’re wrong! 50 googol and 1 is bigger!” But Sam gets mad so he would start shouting and say, “I DID TOO THINK OF THE BIGGEST NUMBER CLARK!!”
Somehow, I don’t think my attempts at an abstract proof worked. Join us next week when I describe the awkward moment in a parent/teacher conference when I had to explain to the math teacher that Clark’s “imaginary numbers” were based on the square root of -1, not numbers who were his invisible friends.