Definition:Power Set/Also known as

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.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.8$. Sets of sets: Example $25$
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 1$: The Language of Set Theory
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $1$: Mappings: $\S 14$
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Sets
• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $1$: Theory of Sets: $\S 2$: Sets and Subsets
• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): Notation and Terminology
• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.4$ Set Notation: Operations on Sets $5)$
• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: Further exercises: $3$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): power set
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): power set