#Type/Definition #Topic/Linear_Algebra

Types: N/A
Examples: 2.3.2 Dial Pad Relation, 2.4.1 Ellipse Relation Domain & Range
Constructions: N/A
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Domain, Range, & More

Let A and B be sets and let R be a relation from A to B. The domain space of relation R is set A.

⟹R⊆A×B

The domain of R is the set

Dom (R)={x∈A:there is at least one y∈B such that (x,y)∈R}.
  • This is the first coordinates from A that are actually used.

The codomain of the relation R is the set

Codom (R)=B.
  • This is the set of all possible second coordinates

The range of the relation R is the set

Rng (R)={y∈A:there is at least one x∈A such that (x,y)∈R}.
  • This is the set of coordinates from B that are actually used.

Remark. The domain is to the domain space as what the range is to the codomain.