You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
\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".
The text was updated successfully, but these errors were encountered:
HermesMarc
changed the title
Computability - Russel's Paradox
Russel's Paradox typo
Sep 25, 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.)
OpenLogic/content/computability/computability-theory/russells-paradox.tex
Lines 15 to 20 in 82a3181
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".
The text was updated successfully, but these errors were encountered: