Let $A$ be a set,
$$\wp^{(0)}(A)=A$$ $$\wp^{(n+1)}(A)=\wp(\wp^{(n)}(A))$$ But what sense does $\wp^{(\alpha)}(A)$ make where $\alpha$ is a limit ordinal number? The most natural way is let $$\wp^{(\alpha)}(A)=\lim_{\xi \uparrow \alpha}\wp^{(\xi)}(A),$$ but what is this 'limit' means? Note that $\wp^{(n)}(A)$ probably not the subset of $\wp^{(n+1)}(A)$.