# Definition:Strictly Maximal Element

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## Definition

Let $\struct {S, \RR}$ be a relational structure.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a **strictly maximal element under $\RR$ of $T$** if and only if:

- $\forall y \in T: x \not \mathrel \RR y$

## Also known as

This **strictly maximal relation** is often referred to as a **maximal relation** in some expositions of this subject.

The appellation **strictly maximal** has been coined by $\mathsf{Pr} \infty \mathsf{fWiki}$ so as to distinguish between this and the more mainstream concept of a **maximal element** which does not preclude $x \mathrel \RR x$.

## Also see

## Sources

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