3
$\begingroup$

Russell's paradox is about a set not in a set itself - but don't all sets are not in sets themselves? $x \in x$ is not true, as {$1,2,3$} $\in$ {$1,2,3$} is not true..

Can anyone explain this?

  • 1
    All *familiar* sets $x$ certainly have the property that $x\not\in x$. If the collection $V$ of all sets is a set, then the set of all $x$ such that $x\not\in x$ is a set. And then Russell's argument leads to a contradiction. One way out is to try to restrict the principles of set construction so that the collection of all sets will not be a set. But at the time of Russell's Paradox, there was the belief that any collection could be called a set, and manipulated using set-theoretic tools.2012-09-18

3 Answers 3