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Russel's Paradox typo #339

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HermesMarc opened this issue Sep 25, 2023 · 1 comment
Open

Russel's Paradox typo #339

HermesMarc opened this issue Sep 25, 2023 · 1 comment

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@HermesMarc
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\item Russell's paradox: let $S = \Setabs{x}{x \notin x}$. Then $x
\in S$ if and only if $x \notin S$, a contradiction.
\emph{Conclusion:} There is no such set~$S$. Assuming the existence of a
``set of all sets'' is inconsistent with the other axioms of set
theory.

I think this should say "then $S \in S$ if and only if $S \notin S$".

Also: Is the "the set of all sets" trying to refer to S? I would have expected S to be described as "the set of all sets that do not contain themself".

@HermesMarc HermesMarc changed the title Computability - Russel's Paradox Russel's Paradox typo Sep 25, 2023
rzach added a commit that referenced this issue Oct 8, 2023
@rzach
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rzach commented Oct 8, 2023

I fixed the typo; the other issue needs more thought. (Briefly: if "the set of all sets" existed, so would S by separation, but this can't easily be explained here. But the whole chapter needs work.)

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