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Wed May 16, 2012 By:

Sir, you have discussed about Russel's Paradox! pls explain what is Russel's Paradox? and sir when will the cbse class 10 results will be out?

Expert Reply
Wed May 16, 2012

Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.

Let be the set of all sets which are not members of themselves. Then is neither a member of itself nor not a member of itself. Symbolically, let . Then iff .

Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “R.” If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics.

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