Difference between revisions of "Russell's Paradox"
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− | '''Russell's Paradox''', | + | The '''Russell's Paradox''', credited to Bertrand Russell, was one of those which forced the axiomatization of set theory. |
==Paradox== | ==Paradox== |
Revision as of 06:32, 25 November 2007
The Russell's Paradox, credited to Bertrand Russell, was one of those which forced the axiomatization of set theory.
Paradox
We start with the property : (
does not belong to
). We define
to be the collection of all
with the property
. Now comes the question: does
have the property
? Assuming it does, it cannot be in itself, in spite of satisfying its own membership criterion, a contradiction. Assuming it doesn't, it must be in itself, in spite of not satisfying its own membership criterion. This is the paradox.