# 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)

- I'm afraid that your statements are directly contradicting ref'd Definition:Partially Ordered Set, and also Definition:Ordered Set. Please pay particular attention to the AKA sections, where it is made clear beyond doubt that only Definition:Ordered Set is to be used, and not poset, for what you describe. — Lord_Farin (talk) 18:56, 19 November 2014 (UTC)

- Oh I remember now, we had this conversations a few years ago. I was never quite sure whether we got it right. Trouble is, there is too much use of "poset" out there to mean a set with an ordering on it of which it is immaterial whether it be partial or not.

- So what is it now then, "ordered set"? --prime mover (talk) 21:46, 19 November 2014 (UTC)

- Ordered set it is. That's as unambiguous as it gets. Unfortunately, it's longer than poset. But then, we have
*infinite*space, so what does it matter? — Lord_Farin (talk) 21:59, 19 November 2014 (UTC)

- Ordered set it is. That's as unambiguous as it gets. Unfortunately, it's longer than poset. But then, we have

Right -- apart from where it appears in category theory (where I'm unsure of my ground) and one or two source work links (Devlin, etc.), all instances of "poset" have as far as I can tell now been changed to "ordered set". --prime mover (talk) 16:33, 6 April 2015 (UTC)

- The references in the category theory department have been incinerated. — Lord_Farin (talk) 16:47, 10 April 2015 (UTC)

- Nice one -- good job. It's a lot more rational than it was. Still plenty to do, of course. --prime mover (talk) 17:55, 10 April 2015 (UTC)