>>12363276If you don't know what "finite" is, then you should probably go with the construction as
>>12363265I.e. define finite to be in bijection with a natural number.
0 and 2:={0,1} are such natural numbers, and so is your 5={0,1,2,3,4}.
And it's in bijection with itself.
There's a range of equivalent and constructive definitions, see pic related.
Kuratowski and the gang also early on tried to give definitions not relying on axiomatizing the collection of all naturals upfront, so there's "more finite" (lel) definitions.
One is:
Given a set S.
>Let B(S) be the smallest subset of P(S) containing the empty set and closed under the operation AA?B for A a subset of S and B a singleton in S disjoint from A. >Then S is finite iff S?B(S).But that's generally much harder to wrap your head around than to exist that N exist in the standard way and putting sets in bijection to its elements (naturals)
