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-of-set-by-inclusion

  S.

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