Definition:Power Set/Also known as

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Power Set: Also known as

The rendition powerset is frequently seen.

Some sources do not use the term power set, merely referring to the term set of all subsets.

Variants of $\PP$ are seen throughout the literature: $\mathfrak P, P, \mathscr P, \mathrm P, \mathbf P$, etc.

Some sources, for example J.A. Green: Sets and Groups, use $\mathscr B$.

Another significant notation is:

$2^S := \set {T: T \subseteq S}$

This is used by, for example, Allan Clark: Elements of Abstract Algebra.

The relevance of this latter notation is clear from the fact that if $S$ has $n$ elements, then $2^S$ has $2^n$ elements‎.