Some of the Likely Many Ways I Was Wrong About Infinity Trees

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I’m now almost two years, and an actual discrete mathematics course, ahead of my apparently-bored-towards-the-end-of-high-school-self, and I’m feeling ready to replace my old mistakes with some fresh new ones. So below are at least some of the reasons I think I was wrong last time, which I will delve into in this post.

1. The diagonal argument is quite clearly order agnostic, and just kind of really good in general.
2. I didn’t define a bijection.
3. There are no irrationals until you get infinitely far down the tree.

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Infinity Trees

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How many numbers are there between zero and one?

Well, quite a few more than there are integers apparently. Uncountably many. Which makes sense really, because it isn’t particularly easy to count them.

Well, we start with zero.
Then there is zero point zero, zero, zero, zero, zero, zero, zero, zero…
Damn.

But, I have thought up a system of accessing them which is confusing me, because I think it might map every real number between zero and one to a unique integer.

Or maybe it doesn’t. Infinity is complicated, irrationals are weird, and I didn’t really do enough research.

I’m also not very good at marketing.

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