Set Theory Part 2: The axioms of ZFC

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So far in this series, we’ve built an intuition for what sets are, but still haven’t given the rules they obey. These are the axioms of ZFC, and now that we’ve developed the proper language in which to state them, we finally have everything we need to introduce these rules.

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  1. cmacypre
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Yes, this is a reupload. The previous version had a mistake in the conditions for the axiom schema of refinement, which has now (hopefully) been corrected. There are also a few cosmetic changes, such as renaming a few variables.

cmacypre-dgwo
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These videos are amazing! I just wonder, what are your end goals with this series? Like, how far are you planning to build set theory?

עדןמזור
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At least on my phone at 2:54 the box for rules for sets was partway off the screen.

peterdebruin
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2:26 Maybe a silly question but why isn't it "c ∈ a AND c ∈ b" instead of " c ∈ a iff c ∈ b"? will it make a difference?

RAyLV