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this post was submitted on 13 Sep 2024
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Cantors diagonal argument and the continuum of the reals is my demiurge. It'd be one thing if it was like a weird tangential fact about the reals, but no, you have to accept choice to construct them in the first place, and then that means that there has to be a well ordering on any subset, and of course, wtf is a well ordering on (0, 1)
It took me until following down the "how do we dodge Gödel's theorem maybe we can use probability or restrict proofs to a subset or something idk." Thoughts of the 1940s logical empiricists that I truly realised how perverse Maths is.
i found out that cantor's diagonal argument is more of a persuasive argument than an actual proof and it's been sort of driving me a bit insane since. math is truly a perverse spiral.
I've been obsessing over axiom of determinacy as a potential replacement for axiom of choice.