Stéfane Fermigier wrote:
On Wed, Mar 4, 2020 at 8:24 AM Steve Jorgensen firstname.lastname@example.org wrote:
Chris Angelico wrote: On Wed, Mar 4, 2020 at 6:04 PM Steve Jorgensen email@example.com wrote:
<snip> https://en.wikipedia.org/wiki/Partially_ordered_set "Partially ordered" means you can compare pairs of elements and find which one comes first. "Totally ordered" means you can compare ANY pair of elements, and you'll always know which comes first. ChrisA Ah. Good to know. I don't think "Partially ordered" actually applies, then, because that still seems to imply that transitivity would apply to comparisons between any given pair of objects. Simply having implementations of all the rich comparison operators does not make that true, however, and in particular, that's not true for sets. Not quite: https://en.wikipedia.org/wiki/Partially_ordered_set#Examples
(see example 2). Or: https://math.stackexchange.com/questions/1305004/what-is-meant-by-ordering-o... S.
Ah! That Wikipedia article is very helpful. I see that it is not necessary for all items in a partially ordered set to be comparable.
Taking one step back out of the realm of mathematical definition, however, the original idea was simply to distinguish what I now understand to be "totally ordered" types from other types, be they "partially ordered" or unordered — not even having a full complement of rich comparison operators or having all but using them in weirder ways than sets do.