Codomain

Codomain
Tag	`0F9JHP8AJN`
URI	`m2://0F9JHP8AJN`
Kind	definition
Writing	W1 stated
MSC	03E20
Defines	Codomain
Uses	Function

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Definition

Let $f \colon A \to B$ be a function. The codomain of $f$ is the set $B$ .

Remarks

Each value $f(a)$ is in the codomain, but not every element of the codomain needs to be a value. The set of values is the range of $f$ . It is a subset of the codomain. The function $f$ is surjective when its range is the whole codomain.

Explanations

L1 human

For $f \colon \mathbb{R} \to \mathbb{R}$ with $f(x) = x^2$ , the codomain is $\mathbb{R}$ . The value $-1$ is in the codomain, but no input gives it.

What this node 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 node is. They do not measure its truth.

What depends on this

42 nodes use this node, directly or through other nodes.

Order of cardinals 01GTP8M5RG
Infinite set 01MKW4R283
Bijective iff it has a two-sided inverse 01VG2A0BHW
Torus 03NM7DZXXC
Continuous bijection from a compact space to a Hausdorff space is a homeomorphism 0430ETCMKD
Homeomorphism 05GZ11PWRY
The integers are countable 066RJJVWH9
Correspondence between equivalence relations and partitions 074482Q7CD
The reals have the cardinality of the continuum 075PM9FH7A
Composition of surjections is surjective 07EH4R3RVQ
Equinumerous sets 08EJHHMB5R
Product of countable sets is countable 08G4XH86JC
Topological embedding 08SVRVHJNY
Schröder–Bernstein theorem 0A9V6RKQG6
Classical definition of probability 0AKNPYQ04R
Finite set 0BBTH3YSZA
The rationals are countable 0DS9KWFDK2
Cardinality of the power set 0GPFKS96T7
Cardinality 0JTGRV4WT4
Discrete uniform distribution 0KYP951QWH
Continuum hypothesis 0MN2MER9WN
Hilbert's hotel 0N3Y8G340X
Birthday problem 0NMWG2PHJ0
Cantor pairing function 0NP5N5PYW5
Cardinal number 0QKPNZKNEA
Cantor set is homeomorphic to the space of binary sequences 0RQ8DHHR8V
Every infinite set has a countably infinite subset 0RWQ5VZ6VQ
Countably infinite set 0SEZ3JGZP7
Bijective function 0SNQEF7Z53
Hypergeometric distribution 0SPBPW3K61
Bertrand paradox 0T0JWJ3M47
Surjective iff it has a right inverse 0TYQNHVB4C
Aleph-null 0V2H5PGJ9B
Isometric isomorphism 0VRD8GC5BM
Inverse function 0W766JAPSN
Cardinality of the continuum 0WC28W9DNM
Circle as a quotient of the real line 0WH1GVBJNH
Cantor's theorem 0WTEMGYV2C
Surjective function 0XKH881BZ7
Order isomorphism 0Y74KN99A5
Comparability of cardinals 0YBHSJMN3J
Countable union of countable sets is countable 0Z8FM54P86

Codomain

Definition

Remarks

Explanations

L1 human

What depends on this

Sources

What links here

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