Linked from

The 10 pages that link to Well-order, each with the reason it gives.

• Ordinal numberRelated: Set-theoretic ordinals encode the order types of well-ordered sets.

• Well-ordering theoremBroader topic: The theorem asserts that every set can be equipped with this kind of order.

• Well-founded relationCompared with: A well-order is a total, reflexive-order setting for the minimal-element property; well-founded relations need not be total.

• Least elementRelated: The defining property generalizes leastness from a whole set to all nonempty subsets.

• Transfinite recursionNarrower topic: Ordinals provide the well-ordered stages that make the recursive definition proceed without circularity.

• Ordinal analysisRelated: Ordinal arguments rely on well-orders and proofs that descending sequences cannot continue.

• Transfinite inductionNarrower topic: The least-counterexample argument relies on the ordinals’ well-ordering.

• Order theoryBroader topic: Well-orders are a distinctive class of orders central to transfinite mathematics.

• Aleph numberRelated: Alephs enumerate precisely the infinite cardinalities represented by well-orderable sets.

• Greatest element and least elementRelated: It guarantees least elements for all nonempty subsets, a stronger condition than having one for the whole set.