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I usually post about MG books here, or books that ride the line between MG and YA. But that doesn't mean I don't read YA. One of my favorite authors is, in fact, the YA writer John Green. Not because I like all of his books equally well (I don't, actually), but because as far as the sheer intelligence of his writing, and his ability to convey things I thought only I thought, I can't remember when I've encountered his like. I'll at least pick up anything he writes; that is for sure.
I recently read his newest novel, The Fault in Our Stars. And it. Is. Brilliant. This year, his (next) Printz may very well come.
However. The book says something that makes what's left of my mathematical mind (which has languished over three or so decades) shudder: That some infinities are bigger than others. That, for example, there are more numbers (not speaking solely of integers, but of all possible rationals and irrationals) between, say, zero and a million than between zero and one.
No, there aren't.
And here I'd really like to diverge from any direct comment on the novel. This is really no longer about the novel. It's just the compulsion that still arises within me every now and then to speak my mathematical piece.
No, some infinities are not bigger than others. Such a notion doesn't make sense. Between zero and one lies an infinite number of fractions and decimals, almost all of them irrational, or non-repeating decimals. 0.5039285715790432... and on and on; you get the picture. No pattern to them. This means there's always another one. And another one. And one more. And yet one more.
For every such number, for any number at all, that lies between zero and a million, you can find one that lies between zero and one to pair with it in a one-to-one correspondence. You will never run out of numbers between zero and one, any more than you'll run out of numbers between zero and a trillion bazillion.
And this is just one of the things that make math, and creation, amazingly cool.