Editing Well-quasi-ordering (section)

==Wqo's versus well partial orders==

In practice, the wqo's one manipulates are quite often not orderings (see examples above), and the theory is technically smoother{{fact|date=March 2017}} if we do not require antisymmetry, so it is built with wqo's as the basic notion. On the other hand, according to Milner 1985, ''no real gain in generality is obtained by considering quasi-orders rather than partial orders... it is simply more convenient to do so.''

Observe that a wpo is a wqo, and that a wqo gives rise to a wpo between equivalence classes induced by the kernel of the wqo. For example, if we order <math>\Z</math> by divisibility, we end up with <math>n\equiv m</math> if and only if <math>n=\pm m</math>, so that <math>(\Z,|)\approx(\N,|)</math>.