You should make clear why a (von Neumann) ordinal needs to be a transitive set (the fact that it should be well ordered (by the unique given relation in ZFC, the membership) is more clear, at least to me). Or simply claim first that all we need are well ordered sets (but there it comes the axiom of choice) and then add a unique well defined set (that is, an ordinal) order isomorphic to that well ordered set
Super interesting video and really understandable, even for me as a set theory beginner. Thank you for sharing!
You should make clear why a (von Neumann) ordinal needs to be a transitive set (the fact that it should be well ordered (by the unique given relation in ZFC, the membership) is more clear, at least to me). Or simply claim first that all we need are well ordered sets (but there it comes the axiom of choice) and then add a unique well defined set (that is, an ordinal) order isomorphic to that well ordered set
Microseconds be like:
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60 Microseconds later:
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10⁶
10^10^100
TREE(3)
Omega