$\exists X (\forall Y (\neg(Y \in X)))$
is whats given in my lecture, but I was wondering, is it the same as
$\exists X (\forall Y (Y \notin X))$
$\exists X (\forall Y (\neg(Y \in X)))$
is whats given in my lecture, but I was wondering, is it the same as
$\exists X (\forall Y (Y \notin X))$
Yes, this is what $\notin$ means. $A \notin B$ is a shorthand for $\neg(A \in B)$.