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Everything about Power set

Mathematical set of all subsets of a set

In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), 𝒫(S), P(S),, or 2S. Any subset of P(S) is called a family of sets over S. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Power setA 5-minute orientation
  2. Skim a recent paper: Finite Control-Set Learning Predictive Control for Power ConvertersInfluential work since 2022
  3. Pick up a classic book: Psychic Warfare - Brain FightingThe most-reprinted book on the subject
  4. Read the landmark paper: Unsettling the Coloniality of Being/Power/Truth/Freedom: Towards the Human, After Man, Its Overrepresentation--An ArgumentCited 4,451 times
  5. Go sideways: Boolean algebras canonically definedA closely related topic
  6. Go sideways: Complete latticeA closely related topic

📖 Definitions

Noun The set whose elements comprise all the subsets of S (including the empty set and S itself).

🗂️ The subject at a glance

  1. Example
  2. Properties
  3. Representing subsets as functions
  4. Relation to binomial theorem
  5. Recursive definition
  6. Subsets of limited cardinality
  7. Power object
  8. Functors and quantifiers

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics