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### Single Idea 15911

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).

Gist of Idea

Ordinals are generated by endless succession, followed by a limit ordinal

Source

report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.52