# Definition:Join Semilattice/Definition 2

## Definition

Let $\left({S, \vee}\right)$ be a semilattice.

Let $\preceq$ be the ordering on $S$ defined by:

$a \preceq b \iff \left({a \vee b}\right) = b$

Then the ordered structure $\left({S, \vee, \preceq}\right)$ is called a join semilattice.