poll: the most important number is
- 028.5%
- 141.9%
- infinity5.3%
- e or pi or some shit24.4%
1,285 votesFinal results
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Conversation
IMO 0 and 1 are the most defensible options by a landslide
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the funny thing about 0 is that in set theory it's used to construct all of the other positive integers. you start with 0 defined as the empty set. then 1 is {0}; that is, it's the set whose only element is 0. then 2 is {0, {0}} etc. these are called the "von neumann ordinals"
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for a pure mathematician 0, 1, and infinity have the special feature that they're the only points that are always defined on the projective line P^1(k) over an arbitrary field k (they're the only points when k = F_2) although that's a bit abstruse
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you might say that they're an implementation of peano numerals, where successor is taken to be this funny function x union {x}. "peano numerals" doesn't really refer to a unique thing, depending on how you think about things
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Wait can't you do the same thing with the empty set? {}, {{{}}, {}}, etc ...? Why does 0 "need" to be here?
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This was my exact justification for choosing 0. And considering the entire purpose and thrust of set theory was describing and justifying a solid foundation for mathematics, it seems to me the clear choice!