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Jul
29
awarded  Popular Question
May
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awarded  Nice Question
Apr
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Sep
13
awarded  Good Question
Jul
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Jan
29
awarded  Notable Question
Apr
30
awarded  Yearling
Oct
22
awarded  Popular Question
Jan
22
accepted Descriptions of sets and the Axiom of Choice
Jan
22
asked Why are linear functions the natural analogue of exponential functions in a tropical semiring?
Oct
11
accepted Solving a maze by taking a random walk
Oct
9
asked Solving a maze by taking a random walk
Aug
31
comment Descriptions of sets and the Axiom of Choice
Another, perhaps less tautologous way I was thinking about the first question was this: if all sets (and thus all functions, I think) are specifiable by some finite formula, then assuming a countable alphabet, there exist only a countable number of functions. But it's typically said that there are an uncountable number of functions on the natural numbers, so I think that means that "most" of these functions require the Axiom of Choice?
Aug
31
awarded  Commentator
Aug
31
comment Descriptions of sets and the Axiom of Choice
I studied basic formal set theory and model theory a while ago (at the level of a standard undergraduate course), and I can look up stuff I've forgotten (though more advanced things like forcing are beyond me), so details would be great -- I'm looking for an explanation on the rigorous side.
Aug
31
asked Descriptions of sets and the Axiom of Choice
Aug
30
accepted What is the set-theoretic definition of a function?
Aug
29
awarded  Yearling
Aug
28
comment What is the set-theoretic definition of a function?
@Asaf: Ha, you got me there! I guess I've seen similar explanations before and yours was better :-), and you gave me at least a partial understanding (though for all I know it's an incorrect partial understanding ;-)).
Aug
28
comment What is the set-theoretic definition of a function?
@Arturo: Cool, yeah, I'll make a separate question after thinking about this a bit more. One last thing: can we prove that AoC is required to prove that such a function exists?