Single Idea 14140

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

For every transfinite cardinal there is an infinite collection of transfinite ordinals, although the cardinal number of all ordinals is the same as or less than that of all cardinals.

Gist of Idea

For every transfinite cardinal there is an infinite collection of transfinite ordinals

Source

Bertrand Russell (The Principles of Mathematics [1903], §290)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.312


A Reaction

Sort that one out, and you are beginning to get to grips with the world of the transfinite! Sounds like there are more ordinals than cardinals, and more cardinals than ordinals.