User:Evgeniy An

Universal set.

I'm free researcher. 10 may 1960.

There are some interesting facts from science.

Mathematics. Set theory.

The set of all sets doesn't exist in Zermelo-Fraenkel set theory.

Proof.

1. Let U is set of all sets. 2. No set is an element of itself. This statement exists in the article "Axiom of regularity - Wikipedia. No set is an element of itself". 3. From (1) - U is set and (2), follows that U doesn't include itself. 4. Contradictory to (1) that U includes all sets. 5. So U isn't a set.

End of proof.

Another facts to be continued...