Russell ParadoxDate: Wed, 3 Jul 1996 00:15:34 +0100 From: Nicolas Weibel Subject: Russell Paradox Hi Dr. Math! I'm looking for the demonstration of the Russell Paradox (there is no ensemble of all ensembles). Thanks a lot... Date: Fri, 19 Jul 1996 16:11:20 -0400 (EDT) Subject: Re: Russell Paradox Nicolas, If you're talking about the same Russell paradox that I know, one of my professors gave an excellent example of the paradox. Here it is... Think about a set A, with an interesting definition: A is the set of all the things that aren't in A , i.e., A = {x : x not in A} Now, consider some element, e. Is e in A or not in A? Let's say e is in A. Then by the definition of A, we must conclude it is not in A, since A is only made up of elements that aren't in it. So it can't be in A. But if e isn't in A, then by definition, e is in A. So e can't not be in A. That's the paradox, at least how it was introduced to me. I know it may be tough to follow this, it is a much easier thing to explain in person, but I hope this helps. You can find a slightly different formulation of the paradox, along with Russell's recollection of how he came up with it at http://www.cut-the-knot.org/selfreference/russell.shtml If you have any other questions or want any clarification, feel free to write again! -Doctor Erich, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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