Definition:Meet (Order Theory)

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This page is about Meet in the context of Order Theory. For other uses, see Meet.


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:

$(1): \quad c \preceq a$ and $c \preceq b$
$(2): \quad \forall s \in S: s \preceq a$ and $s \preceq b \implies s \preceq c$

Also known as

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

Also see

  • Results about the meet operation can be found here.