more from Shaughan Lavine

Single Idea 15912

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure]

Full Idea

Counting a set produces a well-ordering of it. Conversely, if one has a well-ordering of a set, one can count it by following the well-ordering.

Gist of Idea

Counting results in well-ordering, and well-ordering makes counting possible


Shaughan Lavine (Understanding the Infinite [1994], III.4)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.53

A Reaction

Cantor didn't mean that you could literally count the set, only in principle.