The axiom of choice seems trivial, yet it gives rise to Banach Tarski paradox. Monkey confused.
@MorlockP You don't need AoC to make infinity choices if you can supply a rule. Like, if you have a zillion copies of the integers...
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@MorlockP ...you don't need AoC to say 'ok I'll set n_i = i'. But an infinite number of choices *with no rule for choosing* requires AoC. -
@MorlockP Specifically in Banach-Tarski, AoC sneaks in when you need a set of coset representatives of the funky tree subgroup thing.
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.