Science Fair Project Encyclopedia
Set of all sets
In set theory, referring to the set of all sets typically leads to a paradox. Is the set an element of itself, or not? Usually, formal logic disallows the construction of such a set. You can refer to "all sets" in the metalanguage.
The statement "no set is an element of itself" has a quantifier that ranges over all sets.
Although in naive set theory, we can talk of the set of all sets that are not elements of themselves, there appear to be set theories with no contradiction found so far where such a thing as the set of all set exists but the set of all sets that are not elements of themselves doesn't.
See also
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details