TITLE: Is there a common notation of the power set excluding the empty set?
QUESTION [10 upvotes]: 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).

REPLY [3 votes]: I would suggest using something close to standard notation, e.g. $\mathcal{P}_{\lt \omega}(X)$ or $[X]^{\lt \omega}$ is used for the set of finite subsets of $X$, so why not $\mathcal{P}_{\geq 1}(X)$ or $[X]^{\geq 1}$?