Simple but funny paradox :)

[PPH]

But even when "include" had that meaning, the set G couldn't possibly exist, since the empty set also includes itself (all sets include the empty set, right?).  

All sets include themselves. Therefore, the set of sets that don't include themselves is empty. But the empty set also includes itself. Therefore, G cannot exist.

I still don't find anything wrong with G being empty . Even empty set includes itself, as you said, but that's why empty set is not _an element_ in set G and G is indeed empty.

(could we get 'mathematical alphabets' to the forum   )

I just realized I misinterpreted your first post (I just reread my quote in that post, and realized what you were talking about). You're right: I must have misintepreted rncneckel's post. If he were talking about subsets instead of elements, G would be the empty set and there would be no paradox.

(and yeah, my last post was stupid I got confused and mixed the "element" and "subset" thing and wrote a preposterous conclusion)

[Sam_Zen]

(could we get 'mathematical alphabets' to the forum)

If it would be possible to use HTML in a post, mathematical characters can be found in Unicode-set 2200.

[LPChip]

(could we get 'mathematical alphabets' to the forum)

If it would be possible to use HTML in a post, mathematical characters can be found in Unicode-set 2200.

You can also make an image and post it that way