Definition:Meet (Order Theory)

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

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

Then $a \wedge b$, the meet of $a$ and $b$, is defined as:


 * $a \wedge b = \inf \left\{{a, b}\right\}$

Expanding the definition of infimum, one sees that $c = a \wedge b$ :


 * $c \preceq a$ and $c \preceq b$ and $\forall s \in S: s \preceq a \land s \preceq b \implies s \preceq c$

Also known as
Some sources refer to this as the intersection of $a$ and $b$.

Also see

 * Definition:Join (Order Theory)
 * Definition:Meet Semilattice
 * Definition:Lattice