A Set? Or Not a Set? Russel's Paradox and Well-Foundedness (Intro To Math Structures Ex1.2.1)

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Russel's paradox concerns the question, "Is the collection of sets which do not contain themselves as elements a set?". This paradox is a great naive set theory question that gets at the formal set axioms of ZFC set theory, in particular Well-Foundedness, without diving too deep into all the formalism. So is the collection a set? or not a set?
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Please keep making these short form videos man you are an inspiration like no other!!!!

andrewdemos
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my partner actually suggested "the set of all sets that *do* contain themselves", which didn't clearly make a paradox, but is disallowed by ZF axioms, altho I wonder if there is a paradox involved in that

meiliyinhua
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A∈A and A∉A are mathematical operations, like 2+3 and 3*4, rather than descriptions of states. As such they are performed in sequence. Once that sequence is recognized, by grammatical tense and vocabulary like "before" and "after" for example, the paradox disappears.

S includes now all and only those sets which did not include themselves previously. So if it did include itself it does not now, and if it did not then it does now.

The paradox is simply an order of operations problem like 2+3*4.

chrisg