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Enumeration

Definition

An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration depend on the discipline of study and the context of a given problem.

Related concepts

Abstract logic Ackermann set theory Aleph number Algebraic logic Alphabet (formal languages)Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axiom Axiom of Choice Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Bijection Bijective function Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Cantor's diagonal argument Cantor's first uncountability proof Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable Computably enumerable set Computational complexity theory Computer science Concrete category Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Countable Countable set Counting Decidability (logic)Decidable language Decidable set Decision problem Deductive system Denumerable Diagram (mathematical logic)Domain of a function Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Enumerated type Enumeration algorithm Enumerative combinatorics Enumerative definition Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-valued logic Finite model theory Finite set First-order logic First uncountable ordinal Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Graph enumeration Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Identity function Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Index set Index set (recursion theory)Inference Infinite-valued logic Infinite set Information theory Inhabited set Initial segment Injection (mathematics)Injective Injective function Integer partition Integers Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem List List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Mathematical logic Mathematical object Mathematics Metalanguage Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Natural number Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Open formula Operation (mathematics)Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partition of a set Peano axioms Permutation Philosophy of mathematics Positive integer Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional variable Quantifier (logic)Quantifier rank Real number Recursion Recursion theory Recursive set Recursively enumerable Relation (mathematics)Reverse mathematics Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequence Sequent calculus Set (mathematics)Set difference Set theorist Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjection Surjective function Syllogism Symbol (formal)Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Thomas Jech Three-valued logic Timeline of mathematical logic Transfer principle Transfinite induction Transitive set True arithmetic Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Validity (logic)Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Well-order Well-ordered Well-ordering Zermelo–Fraenkel set theory

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