Changes

:<math> S\in S \iff S\not\in S.</math>

:<math> S\in S \iff S\not\in S.</math>

Russel's paradox and others like it can be avoided only at the expense of giving up the idea that any criteria can be used to construct sets. For example in [[Zermelo-Fraenkel]] set theory the construction <math>S=\{T\mid T\not\in T\}</math> would not qualify as [[well-founded]]. Some formulations of set theory would allow such a construction but then S would be a [[proper class]] rather than a set.

Russel's paradox and others like it can be avoided only at the expense of giving up the idea that any criteria can be used to construct sets. For example, in the [[Zermelo-Fraenkel]] set theory, the construction <math>S=\{T\mid T\not\in T\}</math> would not qualify as [[well-founded]]. Some formulations of set theory would allow such a construction but then S would be a [[proper class]] rather than a set.

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