Wqo's Versus Well Partial Orders
In practice, the wqo's one manipulates are almost always orderings (see examples above), but the theory is technically smoother if we do not require antisymmetry, so it is built with wqo's as the basic notion.
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 by divisibility, we end up with if and only if, so that .
Read more about this topic: Well-quasi-ordering
Famous quotes containing the words partial and/or orders:
“The only coöperation which is commonly possible is exceedingly partial and superficial; and what little true coöperation there is, is as if it were not, being a harmony inaudible to men. If a man has faith, he will coöperate with equal faith everywhere; if he has not faith, he will continue to live like the rest of the world, whatever company he is joined to.”
—Henry David Thoreau (1817–1862)
“I’ve got orders to obey, thank God.”
—Robert Bolt (1924–1995)