I am reading Enderton's Set Theorey, in which he showed proof for a theorem: There is no set to which every set belongs. In the proof, he wrote:
Let A be a set; we will construct a set not belonging to A. Let $B=\{x\in A|x\not \in x\}$.
I have no trouble understanding the proof. My question is: Beside the fact that $A$ is a set whose members are $x$, what is $A$?
$A$ is a set of what?