Definition:Well-Ordering/Definition 2
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Definition
Let $\struct {S, \preceq}$ be a ordered set.
The ordering $\preceq$ is a well-ordering on $S$ if and only if $\preceq$ is a well-founded total ordering.
Also see
- Results about well-orderings can be found here.
Sources
- 1993: Keith Devlin: The Joy of Sets: Fundamentals of Contemporary Set Theory (2nd ed.) ... (previous) ... (next): $\S 1$: Naive Set Theory: $\S 1.5$: Relations
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations