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

  • Llituro [he/him, they/them]
    ·
    2 months ago

    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)

    • Mardoniush [she/her]
      ·
      2 months ago

      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.

      • Llituro [he/him, they/them]
        ·
        2 months ago

        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.