For any set $S$, $\mathcal{P}(S)$ denotes the power set of $S$ and $\emptyset \in \mathcal{P}(S)$ always holds. Essentially, I want to denote the set that equals the power set (of some $S$) but excluding the empty set. I was thinking about writing $\mathcal{P}^+$ and defining that (as $\mathcal{P}^+(S) := \mathcal{P}(S) – \emptyset = \mathcal{P}(S)\setminus \{\emptyset\}$), but this could be a common enough thing that someone already established a notation for it.
Wikipedia et al. don't mention anything, but maybe there is something nevertheless. I would prefer to use an established notation if there is one (while still defining what I mean).
Best Answer
I am not aware of any such notation (and in the business of choice functions, one runs a lot into $\mathcal P(S)\setminus\{\varnothing\}$).
It is fine to make your own, but be sure to be consistent about it, and to define it at the beginning of your work.
There is a risk of having too many notations, it may burden the reader. Sometimes just writing it explicitly works just as well. If you're tired of doing that, write a LaTeX macro.