Re: Wait, more than one collective noun?
"A set cannot be a member of itself" -- DavCrav
(Apologies to Bertrand Russell and the very large set [or class] of people whose maths is better than mine if I've got this wrong but I think that ...)
... this is equivalent to saying that "the set of all sets that don't contain themselves" is the same as "the set of all sets" But clearly, because the set of all sets does contain itself, your statement is self contradictory.
In practice I seem to recall it is undecidable - you either say you are working within a system where sets can contain themselves (ZFC) where the ZF refers to Zermelo and Fraenkel and the C stands for 'Choice' (as in the Axiom of), or you say that you aren't.
Bonus AofC joke:
Q) What's yellow and equivalent to the Axiom of Choice?
A) Zorn's lemon.