A join, $\vee$ is an operation defined on elements of a poset $P$ (not necessarily all of them) defined as:

The join (or Least upper bound) of $a, b \in P$ is an element $a \vee b \in p$ such that:

(a) $a \vee b$ is an upper bound of $a$ and $b$: thus $a \preceq a \vee b$ and $b \preceq a \vee b$;

(b) $a \vee b$ is the least such upper bound: i.e., if there exists $c \in P$ such that $a \preceq c$ and $b \preceq c$ then $a \vee b \preceq c$.

Note that, if it exists, a join is necessarily unique.

See also Lattice (algebraic structure)