# Definition:Strictly Well-Ordered Set

## Definition

Let $\left({S, \prec}\right)$ be a strictly totally ordered set.

Then $\left({S, \prec}\right)$ is a **strictly well-ordered set** if and only if $\prec$ is a foundational relation.

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Let $\left({S, \prec}\right)$ be a strictly totally ordered set.

Then $\left({S, \prec}\right)$ is a **strictly well-ordered set** if and only if $\prec$ is a foundational relation.

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