Full Idea
A collection M is 'well-ordered' by a relation < if < linearly orders M with a least element, and every subset of M that has an upper bound not in it has an immediate successor.
Gist of Idea
A collection is 'well-ordered' if there is a least element, and all of its successors can be identified
Source
Shaughan Lavine (Understanding the Infinite [1994], III.4)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.53