Mathematical logic and foundations Definition
Codomain
Builds on Function
Definition
Let be a function. The codomain of is the set .
Remarks
Each value is in the codomain, but not every element of the codomain needs to be a value. The set of values is the range of . It is a subset of the codomain. The function is surjective when its range is the whole codomain.
Reading path
To understand this page from the ground up, read these 14 pages in order. The foundations come first.
Show the path as a graph
- no evidence level
- Element definition
- Proposition concept
- Set definition
- Implication definition
- Predicate definition
- Ordered pair definition
- Existential quantifier definition
- Universal quantifier definition
- Cartesian product definition
- Subset definition
- Uniqueness quantifier definition
- Binary relation definition
- Function definition
- Codomain definition
Where this leads
117 pages build on this one.
- Order of cardinals
- Infinite set
- Bijective iff it has a two-sided inverse
- Torus
- Continuous bijection from a compact space to a Hausdorff space is a homeomorphism
- Homeomorphism
- The integers are countable
- Correspondence between equivalence relations and partitions
- The reals have the cardinality of the continuum
- Composition of surjections is surjective
- Equinumerous sets
- Product of countable sets is countable
- Topological embedding
- Schröder–Bernstein theorem
- Classical definition of probability
- Finite set
- The rationals are countable
- Cardinality of the power set
- Cardinality
- Discrete uniform distribution
- Continuum hypothesis
- Hilbert's hotel
- Birthday problem
- Cantor pairing function
- Cardinal number
- Cantor set is homeomorphic to the space of binary sequences
- Every infinite set has a countably infinite subset
- Countably infinite set
- Bijective function
- Hypergeometric distribution
- Bertrand paradox
- Surjective iff it has a right inverse
- Aleph-null
- Isometric isomorphism
- Inverse function
- Cardinality of the continuum
- Circle as a quotient of the real line
- Cantor's theorem
- Surjective function
- Order isomorphism
- Comparability of cardinals
- Countable union of countable sets is countable
- Translation surface
- Kirkman's schoolgirl problem
- Order type
- Classification of surfaces
- Twelvefold way
- Brouwer's characterization of the Cantor space
- Kolmogorov–Arnold–Moser theorem
- Schwarz–Christoffel mapping
- Latin square
- Teichmüller space
- Minkowski question-mark function
- Fodor's lemma
- Naive set theory
- CW complex
- Skolem's paradox
- Stationary set
- Model theory of algebraically closed fields
- Singular cardinals hypothesis
- Standard map
- Internal set theory
- Cantor's isomorphism theorem
- Carathéodory's theorem on boundary extension
- Arnold's cat map
- Random group
- Steinitz's theorem on algebraically closed fields
- Regular surface
- Cohen's independence of CH
- Action-angle coordinates
- Sinai billiard
- Diamond principle
- Milnor's isospectral flat tori
- Inverse transform
- Set theory
- Combinatorial species
- Orbifold
- Mutually orthogonal Latin squares
- Proper forcing axiom
- Nonexistence of a projective plane of order 10
- Fisher's inequality
- Torus knot
- Interchange of summation order
- Lawvere's fixed-point theorem
- Transcendence degree
- Enumerative combinatorics
- Quasisymmetric map
- Liouville–Arnold theorem
- Doubling on the integers is not an isomorphism
- Gödel's consistency of CH and AC
- Steiner system
- Categorical theory
- Bruck–Ryser–Chowla theorem
- Cardinal characteristics of the continuum
- Erdős–Rado theorem
- Aleph number
- Block design
- Von Neumann–Bernays–Gödel set theory
- Graph embedding
- Cantor algebra
- Cantor space
- Riemann surface
- Easton's theorem
- Fubini's theorem for series
- Euler's thirty-six officers problem
- Pseudo-Anosov map
- Error-correcting code
- Algorithmic randomness
- Torus as a group
- Fisher's exact test
- Vaught conjecture
- Bunimovich stadium
- Maximal torus
- Summation of families over arbitrary index sets
- Martin's axiom
- Beth number
- Regular cardinal
Further reading
- Web https://en.wikipedia.org/wiki/Codomain, lead section
About this page
| Tag | 0F9JHP8AJN |
|---|---|
| URI | m2://0F9JHP8AJN |
| Kind | definition |
| Writing | W1 stated |
| MSC | 03E20 |
| Defines | Codomain |
| Uses | Function |
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What this page needs for W2
- edge instance_of in: one example (0 of 1)
- edge not_instance_of in: one non-example that fails one clause (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.