Left-Total Relation

set-theory

Definition

Left-Total Relation

A relation $R\subseteq A\times B$, from set $A$ to set $B$, is called left-total iff for every element $a\in A$ there is at least one element $b\in B$, i.e.:

$$\forall a\in A:\exists b\in B:(a,b)\in R$$