Setting: I am putting Zoe (5 yo) to bed.

Z: Mom, what comes after one hundred?

Me: One hundred and one.

Z: No, I mean when you’re counting by tens.

Me: One hundred and ten.

Z: But then what comes after one hundred ninety?

Me: Two hundred.

Z: But what comes after nine hundred?

Me: Nine hundred and one.

Z: But by tens.

Me: Nine hundred and ten.

Z: So what comes after nine hundred ninety by tens?

Me: One thousand.

This conversation continued for a very long time, with questions about what comes after one thousand, one thousand ten, one thousand ninety, one thousand one hundred, and so on. I understood fairly quickly that when she asked “what comes after…?” she really wanted to know the name of the next order of magnitude. But for a while I answered her questions very exactly and made her figure out a way to get precisely to what she wanted to know (yes, I can be cruel to my children like that).

In this way, it took her quite a few questions to get to a million, but she did get there eventually. In fact, when she got there she was surprised that a million was bigger than a thousand because I think that she hears the word million much more often somehow.

After that, I took pity on her and told her the words for billion, trillion, quadrillion, and a few more.

Z: So when do we get to googol and googol plex?

I told Zoe that a googol, and especially googol plex don’t come for a while and that there aren’t “names” for all the numbers up to googol plex. She gave me a very confused look and asked, “But don’t numbers go on forever?” I told her that while numbers go on forever, words do not.

This left her pondering for long enough to finally fall asleep. But something tells me that the conversation is not really over…

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About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.

Are you ready for the question of what “infinity plus one” is? When as a child I mentioned the concept to my friend (along with “infinity plus two” and so on), he said, “You’ve invented some new numbers!” May father was not so impressed: the new numbers seemed meaningless to him. Now I try to teach them (in the form “omega plus one” and so forth) to undergraduates in a set-theory course.

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