3 ms·
This is the problem I was given in my set theory class that convinced me that the axiom of choice is really doing something weird. There's also the Banach-Tarsk
by openasocket 4y ago
This is the problem I was given in my set theory class that convinced me that the axiom of choice is really doing something weird. There's also the Banach-Tarski paradox, but the proof for ultafilters is very simple and approachable.
- syzarian 4y agoThe weirdness comes from uncountable sets. Where choice fails you can have models that have equally bizarre results.
- halpmeh 4y agoAt least in my understanding, some of the weirdness of this specific problem comes from the fact that the mathematicians "know" the function. The AoC doesn't necessarily let you know what the function is, it just lets you know that it exists. So if you were to really play the game with infinite mathematician, nearly everyone would lose even with the AoC.