Upper and Lower Bounds

Topics: Discrete Mathematics - poset

---

(definition)

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

• An element $a\in X$ is an upper bound for $B$ if $b⪯a$ $\forall b\in B$
• An element $c\in X$ is a lower bound for $B$ if $c⪯b$ $\forall b\in B$

We use upper and lower bounds to define the supremum and infimum of a subset, as well as the minimum and maximum of said subset.