Power set

The power set of a set is the set of all its subsets, including the empty set and the set itself. For a finite set with n elements, it has 2ⁿ elements.

Set: A collection of distinct objects treated as a single mathematical object. A power set is constructed from a set as its input.
Combinatorics: The branch of mathematics concerned with counting, arrangement, and selection. Counting subsets is a basic combinatorial problem.
Function set: A set whose elements are functions with a specified domain and codomain. Functions from a set to {0,1} correspond to its subsets.
Finite set: A set that has a finite number of elements. Its power set has exactly 2ⁿ members when the set has n elements.
Subset: A set whose every element also belongs to another set. Each member of a power set is a subset of the original set.
Binomial theorem: An identity expanding a power of a sum into terms with binomial coefficients. Summing the counts of subsets of each size gives (1 + 1)ⁿ = 2ⁿ.
Boolean algebra: An algebraic structure with operations analogous to logical conjunction, disjunction, and negation. A power set forms a Boolean algebra under union, intersection, and complement.
Infinite set: A set that is not finite. Its power set cannot be put in bijection with the original set.
Empty set: The unique set containing no elements. It is a subset of every set and always appears in the power set.
Binomial coefficient: The number of ways to choose k elements from a set of n elements. It counts the power-set members having each particular size.

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