Awatmath.2030
net.math
utcsrgv!utzoo!decvax!watmath!bstempleton
Wed Mar 17 13:18:30 1982
Paradox in set theory
Consider :
       "The set of all sets that are not members of themselves"

This set is not all sets clearly, since some sets like the set of ideas
and the set of mathematical objects are members of themselves.

The set is not empty, because the set of Vax computers is not a member of itself.

Yet the set is a paradox, for if it is a member of itself, then it is
not a member of itself, and if it is not a member of itself, then it
is a member of itself.

-The nasty thing about this paradox is that you CAN'T explain it with
conventional set theory as far as I know.

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