Category:Definitions/Ranges (Relation Theory)

This category contains definitions related to Ranges (Relation Theory).

Let $\RR \subseteq S \times T$ be a relation, or (usually) a mapping (which is, of course, itself a relation).

The range of $\RR$, denoted is defined as one of two things, depending on the source.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ it is denoted $\Rng \RR$, but this may be non-standard.

Range as Codomain

The range of $\RR$ can be defined as $T$.

As such, it is the same thing as the term codomain of $\RR$.

Range as Image

The range of $\RR$ can be defined as:

$\Rng \RR = \set {t \in T: \exists s \in S: \tuple {s, t} \in \RR}$

Defined like this, it is the same as what is defined as the image of $\RR$.