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Single Idea 14119

[from 'The Principles of Mathematics' by Bertrand Russell, in 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite ]

Full Idea

It is not at present known whether, of two different infinite numbers, one must be greater and the other less.

Gist of Idea

We do not currently know whether, of two infinite numbers, one must be greater than the other

Source

Bertrand Russell (The Principles of Mathematics [1903], §118)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.122


A Reaction

This must refer to cardinal numbers, as ordinal numbers have an order. The point is that the proper subset is equal to the set (according to Dedekind).