Category:Definitions/Greatest Elements
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This category contains definitions related to Greatest Elements.
Related results can be found in Category:Greatest Elements.
Let $\struct {S, \preceq}$ be an ordered set.
An element $x \in S$ is the greatest element (of $S$) if and only if:
- $\forall y \in S: y \preceq x$
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 $x$.
Pages in category "Definitions/Greatest Elements"
The following 9 pages are in this category, out of 9 total.