more from Bertrand Russell

Single Idea 14146

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers]

Full Idea

We do not know that of any two different cardinal numbers one must be the greater.

Gist of Idea

We aren't sure if one cardinal number is always bigger than another

Source

Bertrand Russell (The Principles of Mathematics [1903], §300)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.323


A Reaction

This was 1903, and I don't know whether the situation has changed. I find this thought extremely mind-boggling, given that cardinals are supposed to answer the question 'how many?' Presumably they can't be identical either. See Burali-Forti.