Definition:Greatest
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Definition
Ordered Set
Let $\left({S, \preceq}\right)$ be a poset.
An element $x \in S$ is the greatest element (of $S$) iff:
- $\forall y \in S: y \preceq x$
That is, every element of $S$ precedes, or is equal to, $x$.
The Greatest Element is Unique, so calling it the greatest element is justified.
Thus for an element $x$ to be the greatest element, all $y \in S$ must be comparable to $x$.
