# Talk:Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing

The confusion, I think, arises from the fact that we define "strictly increasing mapping" to mean what others call an "order embedding". I believe "strictly increasing mapping" usually means $a < b \implies f(a) < f(b)$ and no more. I don't have a vast library to check this against, however. --Dfeuer (talk) 08:48, 22 February 2013 (UTC)

But that is precisely how we have defined strictly increasing mapping. What confusion do you see? --prime mover (talk) 08:52, 22 February 2013 (UTC)
Actually, there is an $\iff$ on Definition:Strictly Increasing/Mapping. Is it a mistake? --Lord_Farin (talk) 08:54, 22 February 2013 (UTC)
So there is - I will need to go back to the source works to check. --prime mover (talk) 08:55, 22 February 2013 (UTC)
fixed --prime mover (talk) 18:10, 22 February 2013 (UTC)

There may be a problem with the current page (though undoubtedly better than what it was before) in that "Poset" is considered ambiguous. — Lord_Farin (talk) 22:12, 22 February 2013 (UTC)

<sarcasm>Yes, let's make the title six pages long.</sarcasm> I actually think our current insistence on partially ordered sets not being totally ordered is the problem. I wonder if one could exhaust one's fingers counting papers that actually rely on that. --Dfeuer (talk) 22:16, 22 February 2013 (UTC)
The initial definition of "poset" was, like many sources that I consulted, used to mean a set whose ordering was at least partial. Thus every toset is a poset whose ordering is a Definition:Connected Relation. But recently it was decided that it was ambiguous and therefore the usage of poset on ProofWiki is undergoing a change to make it mean "partially ordered set that is most definitely not totally ordered. --prime mover (talk) 22:29, 22 February 2013 (UTC)
One has to balance things. IMHO the "to Poset" part doesn't really add anything: just try to read the title without it and judge for yourself. Should the votes be in favour of this shorter option, please take care to adjust links appropriately (it will instigate double redirects). — Lord_Farin (talk) 22:19, 22 February 2013 (UTC)
Ah, that does work. --Dfeuer (talk) 22:21, 22 February 2013 (UTC)
By the way, if you can find ways to help the average high school student understand this theorem/proof and the dual one, that would be amazing. They're so bloody simple and yet so bloody convoluted to explain. --Dfeuer (talk) 22:22, 22 February 2013 (UTC)
I still think the name was perfectly good as it was. Why was it renamed to this unwieldy version? --prime mover (talk) 22:31, 22 February 2013 (UTC)
The previous title didn't mention the important fact that the domain needs to be a toset. — Lord_Farin (talk) 22:33, 22 February 2013 (UTC)

WTH happened "from" to "on"?! Srsly?! — Lord_Farin (talk) 22:36, 22 February 2013 (UTC)

I still dispute that the title has to uniquely and completely specify the result contained therein, if doing so gives an unwieldy title that is difficult to comprehend in a glance. --prime mover (talk) 22:37, 22 February 2013 (UTC)
... oh, and we're up to quadruple redirects in a minute ... --prime mover (talk) 22:37, 22 February 2013 (UTC)

Um what? I started fixing up links and then everything started shifting on me. What's the final answer? --Dfeuer (talk) 22:40, 22 February 2013 (UTC)

This was my final suggestion. If we keep at this, we can delete all the intermediate crap that came with it and that has only existed for less than a day. — Lord_Farin (talk) 22:41, 22 February 2013 (UTC)
This example of too-many-cooks sums up the problem with the approach of changing pages arbitrarily without properly thinking through what we want the thing to do. Worry not, I have done all the appropriate redirection. Can we not have shit like this happening again? --prime mover (talk) 22:57, 22 February 2013 (UTC)
And so we learn to discuss things before acting; the hard way appears inevitable. I've taken the liberty of deleting the intermediate crap. — Lord_Farin (talk) 22:58, 22 February 2013 (UTC)

We haven't finished yet of course. Whoever did the last set of renaming didn't rename the subpages. Remember to do that next time. Don't worry, I'm doing them by hand. Don't nobody else touch till it's done. --prime mover (talk) 23:02, 22 February 2013 (UTC)

... I think that's it now. --prime mover (talk) 23:09, 22 February 2013 (UTC)
I'm sorry for the trouble. --Dfeuer (talk) 23:18, 22 February 2013 (UTC)