# Definition:Meet (Order Theory)

## Definition

Let $\struct {S, \preceq}$ be an ordered set.

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

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

$a \wedge b = \inf \set {a, b}$

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

$c \preceq a$ 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

• Results about meet (and join) can be found here.