Single Idea 14143

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity]

Full Idea

The ordinal representing the whole series must be different from what represents a segment of itself, with no immediate predecessor, since the series has no last term. ω names the class progression, or generating relation of series of this class.

Gist of Idea

ω names the whole series, or the generating relation of the series of ordinal numbers

Source

Bertrand Russell (The Principles of Mathematics [1903], §291)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.313


A Reaction

He is paraphrasing Cantor's original account of ω.