Definition:Meet (Order Theory)

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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 $c = a \wedge b$ 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.


Sources