Definition talk:Totally Ordered Set

I direct recent editors to the statement on this page:


 * As tosets are still posets, all results applying to posets also apply to tosets.


 * So it is usual to use the term poset to mean a set which may be partially or totally ordered, and partially ordered set when we want to make it clear that the set under discussion is definitely not totally ordered.

So it is incorrect to say "the definition of partial ordering excludes total orderings". It does not. At least on this site, the term "poset" is defined specifically to include tosets. This is not a mistake, it is deliberate.

If a source can be found which specifically counterstates this, please let me know so we will be able to tidy this point up, as it has been the source of disagreements before. --prime mover (talk) 22:07, 18 November 2014 (UTC)