Definition
In set theory, the union of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero sets and it is by definition equal to the empty set.
Related concepts
Abraham FraenkelAbstract logicAckermann set theoryAleph numberAlgebra of setsAlgebraic logicAlmostAlphabet (formal languages)Alternation (formal language theory)Alternative set theoryAmorphous setArgumentArithmetices principia, nova methodo expositaArityAssociativeAtomic formulaAtomic model (mathematical logic)Atomic sentenceAutomata theoryAutomated theorem provingAxiomAxiom of adjunctionAxiom of choiceAxiom of constructibilityAxiom of countable choiceAxiom of dependent choiceAxiom of determinacyAxiom of extensionalityAxiom of global choiceAxiom of infinityAxiom of limitation of sizeAxiom of pairingAxiom of power setAxiom of projective determinacyAxiom of regularityAxiom of specificationAxiom of unionAxiom schemaAxiom schema of replacementAxiom schema of specificationAxiomatic systemAxiomatization of Boolean algebrasBanach–Tarski paradoxBertrand RussellBijectionBinary operationBoolean algebraBoolean algebra (structure)Boolean algebras canonically definedBoolean functionBurali-Forti paradoxCantor's diagonal argumentCantor's paradoxCantor's theoremCardinal numberCardinalityCartesian productCategorical theoryCategory (mathematics)Category of setsCategory theoryChurch encodingChurch–Turing thesisClass (set theory)Classical logicCodomainCommutativeCompactness theoremComplement (set theory)Complete theoryComputability theoryComputable functionComputable setComputably enumerable setConcrete categoryConservative extensionConsistencyConstructible universeConstruction of the real numbersConstructive set theoryContinuum hypothesisCountable setDe Morgan's lawsDecidability (logic)Decision problemDedekind-infinite setDeductive systemDiagram (mathematical logic)Disjoint unionDomain of a functionElement (mathematics)Element (set theory)Elementary diagramElementary equivalenceElementary function arithmeticEmpty setEncyclopedia of MathematicsEnumerationEquiconsistencyEquivalence relationErnst ZermeloEuclid's ElementsEuclidean geometryEuropean Mathematical SocietyEven numberExistential quantificationExpression (mathematics)Extension by definitionExtension by definitionsExtension by new constant and function namesExtensionalityFamily of setsFilter on a setFinitary relationFinite-valued logicFinite model theoryFinite setFirst-order logicFixed-point logicForcing (mathematics)Formal grammarFormal languageFormal proofFormal semantics (logic)Formal systemFormation ruleFoundations of geometryFoundations of mathematicsFree logicFree variables and bound variablesFunction (mathematics)Functional predicateFuzzy setGeneral set theoryGeorg CantorGiuseppe PeanoGrothendieck universeGround expressionGround formulaGödel's completeness theoremGödel's incompleteness theoremsGödel numberingHalting problemHereditarily finite setHereditary setHigher-order logicHilbert's axiomsHilbert systemHistory of logicHistory of mathematical logicHistory of set theoryIdentity elementIf and only ifImage (mathematics)Inaccessible cardinalInclusion–exclusion principleIndependence (mathematical logic)Index setInferenceInfinite-valued logicInfinite setInfinite sumInformation theoryInhabited setInjective functionIntegerInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)IsomorphismIterated binary operationJames Pierpont (mathematician)John von NeumannKolmogorov complexityKripke's theory of truthKripke–Platek set theoryKurt GödelLambda calculusLarge cardinalLemma (mathematics)Lindström's theoremList of Hilbert systemsList of axiomsList of first-order theoriesList of formal systemsList of mathematical symbolsList of mathematical theoriesList of set identities and relationsList of statements independent of ZFCLogicLogical biconditionalLogical conjunctionLogical connectiveLogical consequenceLogical constantLogical disjunctionLogical equalityLogical equivalenceLogical truthLogicismLöwenheim–Skolem theoremMany-valued logicMap (mathematics)Martin's axiomMaterial conditionalMathematical logicMathematical objectMetalanguageMiddle FrenchMinimal axioms for Boolean algebraModel complete theoryModel theoryMonadic predicate calculusMonadic second-order logicMorse–Kelley set theoryNP (complexity)Naive set theoryNatural deductionNatural numberNegationNew FoundationsNon-Euclidean geometryNon-logical symbolNon-standard modelNon-standard model of arithmeticOpen formulaOperation (mathematics)Ordered pairOrdinal analysisOrdinal numberOxford English DictionaryP (complexity)P versus NP problemParadoxes of set theoryPartition of a setPaul BernaysPaul CohenPeano axiomsPhilosophy of mathematicsPost-Classical Latin languagePower setPredicate (logic)Predicate (mathematical logic)Predicate logicPredicate variablePrime modelPrime numberPrimitive recursive arithmeticPrimitive recursive functionPrincipia MathematicaProof of impossibilityProof theoryPropositionPropositional calculusPropositional formulaPropositional variableQuantifier (logic)Quantifier rankRecursionRecursive setRelation (mathematics)Reverse mathematicsRichard DedekindRobinson arithmeticRule of inferenceRussell's paradoxSatisfiabilitySaturated modelSchröder–Bernstein theoremSecond-order arithmeticSecond-order logicSelf-verifying theoriesSemantic theory of truthSemantics of logicSentence (mathematical logic)Sequent calculusSet-builder notationSet (mathematics)Set theorySignature (logic)Singleton (mathematics)Skolem arithmeticSoundnessSpectrum of a sentenceSpectrum of a theorySquare of oppositionStrength (mathematical logic)String (formal languages)Structure (mathematical logic)SubsetSubstitution (logic)Substructure (mathematics)SupertaskSurjective functionSuslin's problemSyllogismSymbol (formal)Symmetric differenceSyntax (logic)T-schemaTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTautology (logic)TeXTerm (logic)Term logicTheoremTheories of truthTheory (mathematical logic)Thomas JechThoralf SkolemThree-valued logicTimeline of mathematical logicTransfer principleTransfinite inductionTransitive setTrue arithmeticTruth predicateTruth tableTruth valueTupleTuring machineType (model theory)Type theoryUltrafilter (set theory)Ultrafilter on a setUltraproductUncountable setUndecidable problemUnicodeUninterpreted functionUniqueness quantificationUniversal quantificationUniversal setUniverse (mathematics)UrelementValidity (logic)Variable (mathematics)Venn diagramVon Neumann universeVon Neumann–Bernays–Gödel set theoryWell-formed formulaWillard Van Orman QuineZermelo set theoryZermelo–Fraenkel set theoryZero
143 concepts already in your glossary