Definition:Join (Order Theory)

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $a, b \in S$, and suppose that their supremum $\sup \left\{{a, b}\right\}$ exists in $S$.

Then $a \vee b$, the join of $a$ and $b$, is defined as:


 * $a \vee b = \sup \left\{{a, b}\right\}$

Also see

 * Meet (Order Theory)
 * Join Semilattice
 * Lattice