more from William D. Hart

Single Idea 13460

[catalogued under 4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets]

Full Idea

A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers.

Gist of Idea

'Well-ordering' must have a least member, so it does the natural numbers but not the integers


William D. Hart (The Evolution of Logic [2010], 1)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.23

A Reaction

The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point.