$\exists\text{ set }X:X=X^X$? Given sets A and B, define the set $B^A$ to be the set of all functions A $\to$ B.
My question is: Is there a set X such that X = $X^X$?
Has this something to do with the axiom of regularity?

Hint: 


*

*By a cardinality argument it follows $|X|=1$.

*Now, can such a $X$ satisfy $X = X^X$?

