See soorce fer Russell's paradox

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 [[David Hilbert|Hilbert]], [[Edmund Husserl|Husserl]] an ither members o the [[Varsity o Göttingen]].

Accordin tae naive set theory, any definable collection is a [[Set (mathematics)|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:

:<math>\text{Let } R = \{ x \mid x \not \in x \} \text{, then } R \in R \iff R \not \in R</math>

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[[Category:Bertrand Russell]]
[[Category:Paradoxes o naive set theory]]
[[Category:1901 in science]]
[[Category:Sel-referential paradoxes]]