blanketglossary

Bijection

Definition

In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set is the image of exactly one element of the first set. Given a function f: A-->B, the image of an element a∈A is the element f(a)∈B in the codomain. The pre-image of an element b∈B is any element a∈A in the domain such that f(a)=b. Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.

Related concepts

Abraham Fraenkel Abstract logic Ackermann set theory Aleph number Algebraic function Algebraic logic Almost Alphabet (formal languages)Alternative set theory Amorphous set Analytic function Antonella Cupillari Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Automorphism Axiom Axiom of adjunction Axiom of choice Axiom of constructibility Axiom of countable choice Axiom of dependent choice Axiom of determinacy Axiom of extensionality Axiom of global choice Axiom of infinity Axiom of limitation of size Axiom of pairing Axiom of power set Axiom of projective determinacy Axiom of regularity Axiom of union Axiom schema Axiom schema of replacement Axiom schema of specification Axiomatic set theory Axiomatic system Axiomatization of Boolean algebras Ax–Grothendieck theorem Banach–Tarski paradox Batting order (baseball)Bertrand Russell Bijection, injection and surjection Bijective numeration Bijective proof Binary operation Binary relation Boolean-valued function Boolean algebra Boolean algebras canonically defined Boolean function Burali-Forti paradox Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinal number Cardinalities Cardinality Cartesian product Categorical theory Category (mathematics)Category of groups Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Complex-valued function Computability theory Computable function Computable set Computably enumerable set Concrete category Conservative extension Consistency Constant function Constructible universe Construction of the real numbers Constructive set theory Continuous function Continuum hypothesis Converse relation Countable set Counting Cricket De Morgan's laws Decidability (logic)Decision problem Dedekind-infinite set Deductive system Diagram (mathematical logic)Diffeomorphism Disjoint union Domain of a function Element (mathematics)Element of a set Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Encyclopedia of Mathematics Enumeration Equiconsistency Equinumerosity Equivalence relation Eric W. Weisstein Ernst Zermelo Euclid's Elements Euclidean geometry European Mathematical Society Even number Existential quantification Exponential function Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Factorial Family of sets Filter on a set Fingerprint Finitary relation Finite-valued logic Finite model theory Finite set First-order logic 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)Function composition Function of a complex variable Function of a real variable Function of several complex variables Function of several real variables Function space Functional predicate Functor Fuzzy set Galois correspondence General set theory Geometric transformation Georg Cantor Graph of a function Grothendieck universe Ground expression Ground formula Group (algebra)Group (mathematics)Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditarily finite set Hereditary set Higher-order function Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic History of the function concept Homeomorphism Homomorphism Identity function If and only if Image (mathematics)Implicit function Inaccessible cardinal Independence (mathematical logic)Inference Infinite-valued logic Infinite set Information theory Inhabited set Injection (mathematics)Injective Injective function Integer Integer-valued function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Inverse function Invertible function Isomorphism John von Neumann Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Kurt Gödel Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem Linear function Linear map List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical functions List of mathematical theories List of set identities and relations List of statements independent of ZFC List of types of functions 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)Marshall Hall (mathematician)Martin's axiom Material conditional MathWorld Mathematical logic Mathematical object Mathematics Measurable function Metalanguage Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morphism Morse–Kelley set theory Multiplicative inverse Multivalued function Möbius transformation NP (complexity)Naive set theory Natural deduction Natural logarithm Natural number Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic One-to-one function Onto Open formula Operation (mathematics)Ordered pair Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partial function Partial functions Partition of a set Paul Bernays Paul Cohen Peano axioms Permutation Philosophy of mathematics Polynomial 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 Rational function Rational number Real-valued function Recursion Recursive set Relation (mathematics)Restriction (mathematics)Reverse mathematics Richard Dedekind 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-builder notation Set-valued function Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Smooth function Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Subset Substitution (logic)Substructure (mathematics)Supertask Surjection Surjective Surjective function Suslin's problem Syllogism Symbol (formal)Symmetric difference Symmetric group Symmetric inverse semigroup 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 Thoralf Skolem Three-valued logic Timeline of mathematical logic Total function Total ordering Transfer principle Transfinite induction Transformation (function)Transitive set True arithmetic Truth predicate Truth table Truth value Tuple Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultrafilter on a set Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Unit interval 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 Willard Van Orman Quine Zermelo set theory Zermelo–Fraenkel set theory

149 concepts already in your glossary