Talk:Monotonicity

message: There are now two articles on monotonicity, the other one being monotonic function. Monotonic function is more extensive and contains the general definitions. It might therefore be good to include the "monotonicity" article into the structure of "monotonic function".
I also do not know about the definitions given here: where do we actually deal with "commensurate difference functions" and "equal monotonicity" (which is clearly different from monotonicity in the general sense)? Are there examples? Is this generally accepted terminology (reference books?)? The given notion of "convergence" also needs some explanation/motivation: Where is it applied? How does it compare to all the other concepts of convergence in mathematics?
There is also a problem with redirects. We cannot redirect "monotone function" to "monotonicity" if there is some "monotonic function".
--Markus Krötzsch 13:31, 21 Mar 2004 (UTC)
replies: text: Fixed the redirects and links to this page. Actually all links to this page really wanted the monotonicity from order theory as given in monotonic function or the calculus version (also given there). No articles seem to refer to the actual content of this page here... --Markus Krötzsch 14:17, 21 Mar 2004 (UTC)

message: This page makes little sense to me.
#"Monotonicity" should point to monotonic function (in fact one could make an argument that "monotonic function" should be renamed to "monotonicity", and "monotonic function" should redirect to it.)
#It introduces terminology "equal monotonicity" and "opposite monotonicity", which I've never heard used before. The usual terms are "monotone" (or "order-preserving) and "antitone" (or "order-reversing") respectively.
#It uses an odd definition for monotonicity: x < y  -> f(x) ≤ f(y) instead of the usual (and equivalent): x ≤ y  -> f(x) ≤ f(y).
#It defines a generalized notion of convergence for functions between posets. However I've never seen this definition before and I wonder where this definition has been used before.
I propose the following:
#Merge with Monotonic function whatever needs merging from this article. (I've already merged, and generaslized, the bit about constant maps — the only part which seems relevant to me.)
#If the generaslized convergence stuff is important, then either merge it with limit (mathematics) say, or move it to it's own article perhaps.
#Redirect this article to monotonic function.
Comments? Paul August  ☎ 16:52, Mar 8, 2005 (UTC)
:I don't find the "odd" definition so odd; the two definitions mentioned are obviously exactly equivalent.  Also, the terms "monotone increasing" and "monotone decreasing" are commonplace, but I've seldom heard or seen "antitone". Michael Hardy 02:12, 9 Mar 2005 (UTC)
replies: text:  The reason probably is that "monotone decreasing" is far more common in functional analysis, while it is typically not used in order or lattice theory. Other names which are also common in the latter areas are "order-reversing" and "anti-monotone". Etymologically, "antitone" probably is derived from the latter of these, and may thus be the youngest of these terms. I like it because (a) its short and (b) it has a unique spelling (computer searches may care if someone searches "order reversing" instead of "order-reversing") (c) there is no other notion named like this. --Markus Krötzsch 14:44, 14 Mar 2005 (UTC)

text: I completely agree with the objections and the proposed solution. Someone be bold please. --Markus Krötzsch 14:44, 14 Mar 2005 (UTC)
thread_title:  This page makes little sense