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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 $\wp^{(n+1)}(A)$.

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    Is that symbol $\wp$ often used for power set?2012-06-14
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    @GEdgar Yes, $\mathcal{P}$ and $\wp$ are both familiar. [Wiki_powerset](http://en.wikipedia.org/wiki/Power_set)2012-06-14

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