Single Idea 17904

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

Full Idea

Any set has k members if and only if it can be put into one-to-one correspondence with the set of numbers less than or equal to k.

Gist of Idea

A set has k members if it one-one corresponds with the numbers less than or equal to k

Source

Paul Benacerraf (What Numbers Could Not Be [1965], I)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.275


A Reaction

This is 'Ernie's' view of things in the paper. This defines the finite cardinal numbers in terms of the finite ordinal numbers. He has already said that the set of numbers is well-ordered.