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?

Asked by  | 16th May, 2012, 12:51: PM

Expert Answer:

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.

Answered by  | 16th May, 2012, 06:05: PM

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