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.