A class is a generalized set invented to get around Russell's antinomy while retaining the arbitrary criteria for membership which leads to difficulty for sets. The members of classes are sets, but it is possible to have the class of "all sets which are not members of themselves" without producing a paradox (since is a proper class (and not a set), it is not a candidate for membership in ).

The distinction between classes and sets is a concept from von Neumann-Bernays-Gödel set theory.

See also

Aggregate, Proper Class, Russell's Antinomy, Set, Type, von Neumann-Bernays-Gödel Set Theory

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References

Gonseth, F. "Faiblesse des idées générales de classe et d'attribut." §108 in Les mathématiques et la réalité: Essai sur la méthode axiomatique. Paris, France: Félix Alcan, pp. 259-261, 1936.

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Set Class

Cite this as:

Weisstein, Eric W. "Set Class." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SetClass.html

Subject classifications