KnowraEmpty setEmpty setThe unique set containing no elements, denoted ∅ or {}. It is a subset of every set and has cardinality zero.BriefConnectSet: A collection of distinct objects treated as a single mathematical object. The empty set is the unique set with no members.Union: The set of elements belonging to at least one of two or more sets. Union with the empty set leaves any set unchanged.Singleton set: A set containing exactly one element. It contrasts with the empty set by having one member rather than none.Vacuous truth: A universal statement that is true because its domain contains no counterexamples. Claims about every element of the empty set are true vacuously.Membership relation: The relation that states whether an object is an element of a set. No object stands in this relation to the empty set.Intersection: The set of elements common to two or more sets. Intersecting any set with the empty set produces the empty set.Empty string: A string containing zero symbols, distinct from a string containing a blank symbol. Both contain nothing of their respective kinds, but a string is not a set.Mathematical induction: A proof method that establishes a base case and propagates a result through natural numbers. Recursive definitions often begin with an empty-set base case.Subset: A set whose every element is also an element of another set. With no elements to violate inclusion, the empty set is a subset of every set.Power set: The set of all subsets of a given set. The empty set has exactly one subset: itself.Show all 20Linked from 40 pagesSet theoryBroader topic: It anchors constructions that build larger sets from nothing.Lebesgue integralRelated: Null sets explain why pointwise differences can be irrelevant to integration.Interval (mathematics)Compared with: Under the between-points definition, the empty set qualifies as an interval vacuously.Finite setBroader topic: It is finite with cardinality zero when zero is included among the natural numbers.Lebesgue measureRelated: Lebesgue measure treats sets of measure zero as negligible in integration and almost-everywhere statements.Baire category theoremCompared with: Meagreness concerns topology, not measure; a set can be meagre without being null, or vice versa.Measure spaceBroader topic: Zero size does not imply emptiness in a measure space.Almost sure convergenceRelated: The exceptional outcomes where convergence fails must form a null set.Show all 40