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zfc doesn't have functions, so you are building something new on top of it. Also, I am not sure successor function is enough for PA.
by andriy_koval 1mo ago
zfc doesn't have functions, so you are building something new on top of it.
Also, I am not sure successor function is enough for PA.
- Smaug123 1mo agoIt simply does have functions. According to ZFC, a function is a set whose members are pairs, such that no two different pairs have the same first element. I mean this quite seriously: have you considered reading any first course in set theory?
- andriy_koval 1mo ago> According to ZFC, a function is a set whose members are pairs, such that no two different pairs have the same first element. Can you cite where did you get this?
- Smaug123 1mo agoAs I have said a few times now, you should read any first course in set theory. I’m quoting my third-year notes from Cambridge there, but essentially every intro to set theory will say the same. (I’m sure someone will find a single counterexample that does it somehow differently.)
- andriy_koval 1mo agoYour third year notes from Cambridge has very low authority to me
- jasomill 1mo agoFormally, a function f is a relation between sets A and B such that, for all x in A and u,v in B, f(x) = u and f(x) = v implies u = v. It's just a definition. Authority is, as the parent suggests, any introduction to set theory.
- andriy_koval 1mo ago> Formally, a function f is a relation discussion was if zfc has functions at all, not sure why you put relation here.
- jibal 1mo agoThe guy's remarkable response makes clear that he's a clueless troll.