Answer by Timothée Jinsheng Yu for Formally how do we view finite sets
In modern mathematics, there's nothing but sets (well, we have proper classes which aren't sets but they just appear in category theory or NBG set theory). That is to say, we discuss things under...
View ArticleAnswer by spaceisdarkgreen for Formally how do we view finite sets
This is actually very subtle, in fact IMO one of the most underrated subtleties to come out of mathematical logic.To get the unsurprising part out of the way first, the way we do it is, as you suggest,...
View ArticleFormally how do we view finite sets
This might be silly, but I have been thinking about how we would work with finite sets very formally.So, $\{1,2,3,\cdots,n\} = \{k \in \mathbb{Z}^+ \mid k \leq n\}$ gives a representee for which any...
View ArticleAnswer by Hope Duncan for Formally how do we view finite sets
While less intuitive upfront, using the definition that $A$ is a finite set if and only if $\langle P(A), \subseteq \rangle$ is well-founded may help you here!
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