Interesting Paradox

[Sidoh]

Gottlob Frege said (in essence) that any set either:
  a) Contains itself
  b) Doesn't contain itself

Makes sense, right?

Later on, Bertrand Russell pointed out this interesting paradox:

Let A be a set containing all sets that don't contain themself.  Now, as yourself, should A be a member of itself?  It doesn't contain itself, so it should, right?  Now, it does contain itself, so it can't be in there.  That's the paradox!

Incidentally, I guess after Russell pointed this out to Frege, he came close to committing suicide.  It goes to show: inventing axioms is serious business. :|

[iago]

Heh, I remember learning about an internal contradiction in set theory one time. That may have been it :)

[Joe]

Cool.. :)

[Ender]

Haha, that's so awesome.