Re: Is {} and element of all sets?


Hatto von Aquitanien wrote:
Owen wrote:

It is clearly false to say that {} e {}.
There is no set that is a member of the empty set.

Therefore, you are incorrect to say that {} is a member of all sets!

If I *define* {} as the set that has no members other than itself, then you
are wrong.

But I don't think you can do that and arrive at a self-consistent
set theory. Specifically, I don't think there's such a thing as a
set theory that allows sets to be members of themselves.

I haven't read this thread in detail, but I'm sure somebody would
have mentioned Russell's Paradox in that connection.

- Randy

.

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