Single Idea 17760

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

Full Idea

There may be several ordinals for the same cardinality. ...Two ordinals can represent different ways of well-ordering the same number (aleph-0) of elements.

Gist of Idea

Two infinite ordinals can represent a single infinite cardinal

Source

Michal Walicki (Introduction to Mathematical Logic [2012], 2.3)

Book Reference

Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.89


A Reaction

This only applies to infinite ordinals and cardinals. For the finite, the two coincide. In infinite arithmetic the rules are different.