Minimum and Maximum

Topics: Discrete Mathematics - poset

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(definition)

Let $(X,⪯)$ be a poset and let $B\subseteq X$

• An element $x\in X$ is the maximum of $B$ if $x$ is an upper bound and $x\in B$
• An element $y\in X$ is the minimum of $B$ if $y$ is a lower bound and $y\in B$