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Single Idea 15911

[filed under theme 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 Ref

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

The 2 ideas from 'Grundlagen (Foundations of Theory of Manifolds)'

15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]