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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are these meaningfully different from Peano numerals?
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Replying to
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
I'd say Peano numerals are a theory, while von Neumann numerals are a model of Peano numerals constructed inside set theory
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