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On Tue, 2003-04-08 at 22:59, Christophe Grandsire wrote:
> Which is actually a corollary of the Christophe Grandsire Law of Existence: if
> you can imagine something, it exists, has existed or will exist somewhere in
> the multiverse ;))) .

How about the set of all sets that don't belong to themself?* Does that exist
somewhere in the multiverse? If so, how?

* This is an impossible set. If it doesn't belong to itself, then
it satisfies the condition and belongs to itself, which means it doesn't satisfy
the condition, and so it doesn't belong to itself, and we're back to the initial
one again. Apparently the guy who came up with this set, whose name I've
forgotten, went off to write a _Principia Mathematica_ and took a lot of pages
to prove that 1+1=2, which only makes me *want* to be the first person one of
my Maths Lecturers has ever met whose attempted to read the thing. Unfortunately,
I doubt I'd understand most of it...

Tristan (has come to the conclusion that mathematicians *must* have too much
time on their hands to come up with things like that... And then to prove that
1+1=2...)