puzzling out the proofs for concepts so utterly fundamental to math by myself that it’s like if Genesis 1:3 was And God said, 'Let there be integer,' and there was integer
puzzling out the proofs for concepts so utterly fundamental to math by myself that it’s like if Genesis 1:3 was And God said, 'Let there be integer,' and there was integer
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.