Definition:Right-Total Relation

Definition
Let $S$ and $T$ be sets.

Let $\mathcal R \subseteq S \times T$ be a relation in $S$ to $T$.

Then $\mathcal R$ is right-total :
 * $\forall t \in T: \exists s \in S: \tuple {s, t} \in \mathcal R$

That is, every element of $T$ is related to by some element of $S$.

That is, :
 * $\Img {\mathcal R} = T$

where $\Img {\mathcal R}$ denotes the image of $\mathcal R$.

Also known as
A right-total relation can also be referred to as surjective or onto.

Also see

 * Definition:Left-Total Relation


 * Inverse of Right-Total Relation is Left-Total


 * Definition:Surjection: a right-total mapping


 * Surjection iff Image equals Codomain