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The 34 pages that link to Ordinal number, each with the reason it gives.

• Set theoryRelated: Ordinals formalize transfinite sequences and support recursive definitions.

• Natural numberRelated: Natural numbers can name finite positions as well as quantities.

• Georg CantorRelated: Cantor developed transfinite ordinals to describe positions beyond every finite number.

• Continuum hypothesisRelated: The cardinal aleph-one is defined using the least uncountable ordinal.

• Well-founded relationRelated: Ordinals provide canonical well-founded orders for measuring stages and ranks.

• Cumulative hierarchyRelated: Ordinals index the stages, including successor steps and limit stages.

• Total orderRelated: Ordinals are compared by a canonical total order that reflects their order types.

• Axiom of unionRelated: For a limit ordinal, union combines all earlier ordinals into that ordinal.

• Gödel's constructible universeRelated: Ordinals index the stages of L, including its limit stages.

• InfinityRelated: Ordinals extend counting to infinite orderings, unlike cardinal numbers, which measure size.

• Chain (order theory)Related: Well-ordered chains provide the order types represented by ordinals.

• Axiom of constructibilityRelated: The stages of L are indexed by ordinals, continuing through the entire ordinal class.

• Felix HausdorffRelated: Hausdorff studied ordinal arithmetic and transfinite order types.

• Goodstein's theoremRelated: Replacing each sequence term's base with omega yields a strictly descending ordinal measure.

• Order theoryRelated: Ordinals classify well-orders up to order isomorphism.

• Von Neumann–Bernays–Gödel set theoryRelated: The class of all ordinals is a proper class in NBG, not a set.

• Number (mathematics)Related: Ordinals capture position and ordering, a role distinct from measuring quantity.

• Aleph numberRelated: Ordinal indices specify which aleph appears in the sequence.

• Erdős–Rado theoremRelated: Ordinal-indexed notation distinguishes the finite-subset sizes in partition relations.

• Axiom of limitation of sizeRelated: Ordinals index the cumulative hierarchy and help formalize the universe of sets.

• Mostowski collapse lemmaRelated: The collapse identifies well-founded extensional linear orders with ordinal membership structures.