Quote Originally Posted by Xei View Post
No, for Russel's paradox to work, you need to be considering the SET OF SETS which are not elements of themselves. There's nothing wrong with just a set on its own that is not an element of itself. In fact the definition of number I provided comes directly from Russell himself (c.f. An Introduction to Mathematical Philosophy). And Russell banished such paradoxes from his foundation by ruling out putting sets inside sets (this basically banishes self-reference), so in fact all sets are trivially not members of themselves ({}, N, whatever), precisely because they are sets, and thus by definition can't be found inside themselves, as 'themselves' are not allowed to contain any sets.
Okay well that clears a lot of shit up then. So if
  • the "law of sets" or whatever banishes sets from basically being meta
  • sets contain elements
  • sets are defined by the unique properties of their elements


why the fuck is 0 even considered a set? Is it not a rule that all sets should be mappable? Isn't it inevitable the rule exists considering the essence of an element as well as how the concepts "set" and "element" are inseparable?

Quote Originally Posted by Xei View Post
The number 0 is defined as those sets which can be put into a one-to-one mapping with {}, or '∅', the set of no elements
This definition seems pretty meaningless and if anything is a contradiction.

As a disclaimer, I'm only asking you why because I assume my question is probably elementary and that you are way more fluent in math than I