Okay,
So I'm no Mathematician, but I do need some help. Is there any way to make a power set that contains a set containing a set containing some element? The form that I'm looking for is: $\{\{b\}\}$
Doing something like: $\mathcal{P}(\{b\})$ gives me: $\{\{\},\{b\}\}$ which is close.
Doing something like: $\mathcal{P}(\{\{b\}\})$ gives me: $\{\{\}, (b)\}$ which I do not understand.
The full context of the problem is: I'm looking for a the smallest set whose power set contains the collection of sets given. The collection of sets I'm working on looks like: $\{\{a\},\{\{b\}\},\{a,b\}\}$. I've tried $\mathcal{P}(\{a,b\})$ and $\mathcal{P}(\{a,\{b\}\})$ and $\mathcal{P}(\{a,b,\{\}\})$ but I can't see how to get $\{\{b\}\}$. Any help would be appreciated!
Thanks.