Steve Jorgensen 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. > 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.
Ah. Maybe I'm arguing against a different point than what you were making then. Just because sets are not partially ordered does not mean that "partially ordered" is not a useful distinction in addition to "totally ordered". In that case, maybe the hierarchy would be something like… * ProtoOrdered (or ProtoOrderable): Orderability is explicit and never inferred. Unordered unless also a subclass of PartiallyOrdered or TotallyOrdered. * * PartiallyOrdered * * * TotallyOrdered An class that does not directly or virtually subclass any of those but implements all the rich comparison operators would be treated as an inferred virtual subclass of `TotallyOrdered`. _______________________________________________ Python-ideas mailing list -- python-ideas@python.org To unsubscribe send an email to python-ideas-le...@python.org https://mail.python.org/mailman3/lists/python-ideas.python.org/ Message archived at https://mail.python.org/archives/list/python-ideas@python.org/message/7FV27SQYFR6M66JHHYMFW7EDKHXNJ3MJ/ Code of Conduct: http://python.org/psf/codeofconduct/
