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Single Idea 13653

[from 'Foundations without Foundationalism' by Stewart Shapiro, in 4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets ]

Full Idea

A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element.

Gist of Idea

'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element

Source

Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3)

Book Reference

Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.106


A Reaction

So there is a beginning, an ongoing sequence, and no retracing of steps.