Russell's paradox

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In the foondations o mathematics, Russell's paradox (an aa kent as Russell's antinomy), discovered bi Bertrand Russell in 1901, shawed that some attemptit formalisations o the naive set theory creatit by Georg Cantor led tae a contradiction. The same paradox haed been discovered a year afore bi Ernst Zermelo but he did nae publish the idea, which remained kent anly tae Hilbert, Husserl an ither members o the Varsity o Göttingen.

Accordin tae naive set theory, any definable collection is a set. Let R be the set o aw sets that are nae members o themselves. If R is nae a member o itsel, then its definition dictates that it must contain itsel, an if it contains itsel, then it contradicts its ain definition as the set o aw sets that are nae members o themsels. This contradiction is Russell's paradox. Seembolically: