My brain is working completely fine today and I'm feeling very normal which is why I'm just cycling and cycling and cycling on the comparable magnitudes of infinities.

There are infinite even numbers, odd numbers, and integers. The even number and odd numbers are the same size, but the integers are larger. Counting numbers (positive integers) and odd numbers are the same size. Fractions are way larger than integers — they have a whole extra dimension! But all those collections of numbers are the smaller size of infinities: the countable ones.

The real numbers are uncountable, and so much bigger than any of those, even the multidimensional fractions, despite being all on a line. But the complex numbers are also uncountable, but with a whole dimension beyond the real numbers.

What a weird concept! (And this is just a concept, numbers aren't real. They are useful, though.) Numbers are nowhere near as weird as brains are, except Banach-Tarski, which calls into question the whole idea that numbers are useful for determining how much of something there is.

And I know someone got excited when I started talking about infinities and was waiting for it so here you go: "biject". You're welcome.

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