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I have no idea where you got this from but your statements don't follow any form of logic I'm familiar with. If V = {x | x not in x}, then if V contains itself
by banachtarski 11y ago
I have no idea where you got this from but your statements don't follow any form of logic I'm familiar with.
If V = {x | x not in x}, then if V contains itself, V is not in V (and vice versa) is an obvious contradiction. Your new set S doesn't help in the slightest.
Fixing it is emphatically "not easy" and mathematicians generally rely on the ZFC axiomation (although several other possibilities were proposed).
- Shaniqua 11y agoIt's no big deal if you don't admit universal set or anything other than ZFC.
- johntb86 11y agoIt took 16 years (1901-1917) to get from russell's paradox to a set theory which didn't allow it, but which was able to create a lot of interesting and useful sets (ZF). So it seems like a big deal. And we still can't talk about "the set/collection/whatever of all sets" in the language of ZFC, so we're still missing out.