Once upon a time — long before WiFi and the days of “Ask Siri” — I was egging on a precalculus class to memorize the definition of a mathematical function.

One young lady cried out in anguish, “But can you PLEASE explain that in Regular English!”

I had already given several examples. I knew she had taken notes. And the rest of the class was clearly relieved that she’d bravely stepped forth with her request….

So I said that I would try. But first, I said, I wanted them to work out how they would explain to someone, in Regular English, what a number is. Not so much, I amplified, what a number DOES, but what a number IS.

They worked very hard. They thought, they argued, they grew frustrated, they broke into gales of laughter, they invented science fiction plots, and they realized they couldn’t do it….

But best of all, they came to understand that a formal definition is really hard to construct, and that once you’ve got one, there’s really no other way to explain things completely.

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