more from William D. Hart

Single Idea 13458

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

Full Idea

A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b.

Gist of Idea

A partial ordering becomes 'total' if any two members of its field are comparable


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

Book Reference

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

A Reaction

See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition.

Related Idea

Idea 13457 A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD]