Russell, with his paradox, proves that the set $\{x:x\notin x\}$ of all sets that are
not members of themselves doesn't exist.
So, he demonstrates that the set $\{x:p(x)\}$ doesn't exist necessary (it will not exist
if $p(x)$ leads to a contradiction).

But Zermelo answers (axiom of subsets):

> 
> If the set $A$ exists, and if $p$ is a predicate, then the set $\{x \in A : p(x)\}$
>  of all elements in $A$ satisfying $p$ also exists.
> 
> 
> 

According to axiom of subsets, the set $W = \{x \in \mathbb{R} : x \notin x\}$ exists.
But I don't see what this set is.
For instance, do we have $\pi \in W$ (i.e $\pi \notin \pi$)?