What does a subset of \(\pow(A)\) look like? Notice that \(\{2\} \not\subseteq \pow(A)\) because not everything in \(\{2\}\) is in \(\pow(A)\text{.}\) But we do have \(\{ \{2\} \} \subseteq \pow(A)\text{.}\) The only element of \(\{\{2\}\}\) is the set \(\{2\}\) which is also an element of \(\pow(A)\text{.}\) We could take the collection of all subsets of \(\pow(A)\) and call that \(\pow(\pow(A))\text{.}\) Or even the power set of that set of sets of sets.
in-context