# Definition:Strictly Well-Ordered Set

## Definition

### Definition 1

Let $\struct {S, \RR}$ be a strictly totally ordered set.

Then $\struct {S, \RR}$ is a strictly well-ordered set if and only if $\RR$ is a strictly well-founded relation.

### Definition 2

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

Let $\RR$ be a strict well-ordering on $S$.

Then $\struct {S, \RR}$ is a strictly well-ordered set.