Talk:Residuated mapping

The words "monotone" and "isotone" are both used in this article. I believe that they are synonymous -- is there a reason for the distinction? Richard Pinch (talk) 06:23, 5 July 2008 (UTC)


 * I checked (see article reference Golan) -- they're meant to be the same. Richard Pinch (talk) 06:42, 5 July 2008 (UTC)


 * They are (see Monotonic_function. T.S. Blyth prefers isotone. VasileGaburici (talk) 09:51, 12 July 2008 (UTC)

Please don't add page numbers to the References section. Put those in the Notes section so the same reference can be easily cited multiple times with different page numbers. VasileGaburici (talk) 14:01, 1 September 2008 (UTC)


 * Well, now that there's a Notes section that request makes sense, although it is by no means mandatory: look at the References section in Scientific citation guidelines. See in particular "When not to use inline references" in that article.  Richard Pinch (talk) 17:55, 1 September 2008 (UTC)


 * That worked when we didn't have 5 references for this short article. Now there are sentences like "It can be shown..." with no clear indication as to where the proof is found in those 5 references. VasileGaburici (talk) 19:45, 1 September 2008 (UTC)

As far as I can see, the floor function mentioned in the Example section is *not* itself residuated (since its pre-images are not principal down-sets), whereas it is in fact the residual mapping of the natural embedding of Z into R. In contrast, the *ceiling* function from R to Z (with the usual order in each case) is residuated, with residual mapping the natural embedding of Z into R. Ahangler (talk) 09:36, 17 February 2010 (UTC)