Chris Angelico wrote:
> On Wed, Mar 4, 2020 at 6:04 PM Steve Jorgensen [email protected] 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.
If we consider just the sets `{1, 2}` and `{1, 3}`, …
```
In [1]: {1, 2} < {1, 3}
Out[1]: False
In [2]: {1, 2} >= {1, 3}
Out[2]: False
```
Neither is a subset of the other, so both of those tests return `False`.
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