Talk:Reflexive Closure of Relation Compatible with Operation is Compatible

A preordering as defined on this site is already reflexive. It is defined (you will see it if you click on the link for Definition:Preordering) as being a relation which is reflexive and transitive.

If you are using a definition of preorder which does not match this, then (a) you need to define exactly what it is, and (b) you need to give it another name, because what you're talking about is not it. --prime mover (talk) 15:32, 6 January 2013 (UTC)


 * Sorry, I was for some reason convinced it said transitive and antisymmetric (although surprised by that). That's a rather different matter and I will rename pronto. --Dfeuer (talk) 16:00, 6 January 2013 (UTC)


 * You will find there is already a series of pages which tread the same ground that you are working on. In particular, the relation between $\prec$ and $\preceq$ is established rigorously and there should be absolutely no need for the construct $\preceq = \prec \cup \Delta_S$ which makes my brain hurt.


 * If you use the term "strict ordering" to refer to an antireflexive transitive antisymmetric relation (which is I believe what you are requiring $\prec$ to be, you will save yourself (and the reader) a lot of unnecessary work. --prime mover (talk) 16:07, 6 January 2013 (UTC)


 * Lord_Farin invoked your name earlier when I was looking for info on relations compatible with operations and you didn't speak up, so I really hope that wasn't all duplicate work. Where might I find the info on the relationship between $\prec$ and $\preceq$? --Dfeuer (talk) 16:17, 6 January 2013 (UTC)


 * I didn't speak up because I didn't notice the posting. Besides, as it was discussing what I believed to be preorderings not strict orderings, I didn't recognise the work as being stuff that I had already addressed.


 * Try looing in order theory. Ordering is Strict Ordering Union Diagonal Relation is a place to start. Then that will give you an idea of what terminology to use. --prime mover (talk) 16:22, 6 January 2013 (UTC)


 * I don't care about that. That's just the tail end of the work I've been doing. I'm much more concerned about all the rest of the proofs I created in Category:Compatible Relations. --Dfeuer (talk) 16:26, 6 January 2013 (UTC)


 * I'll leave you to explore then. I have other stuff I'm doing at the moment. --prime mover (talk) 16:50, 6 January 2013 (UTC)