Stéfane Fermigier wrote:
> On Wed, Mar 4, 2020 at 8:24 AM Steve Jorgensen ste...@stevej.name wrote:
> > Chris Angelico wrote:
> > On Wed, Mar 4, 2020 at 6:04 PM Steve Jorgensen
> > ste...@stevej.name 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.
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