Talk:Floor of m+n-1 over n

I see the "Example" subpage, and I'm not sure what to think of it. It certainly marks a departure from the expository style we've had in the past. In general I think we've never aimed to include with a theorem any applications of it. Probably because we don't want or need to fix one approach towards a proof. Maybe the "what links here" and the source flows ought to be enough.

For identities like the ones on this page I guess it's useful to have some aggregation page (like we have for trig identities) because otherwise it's hard to find a specific one. Also because our internal search functionality is exceptionally poor. &mdash; Lord_Farin (talk) 04:00, 27 August 2016 (EDT)


 * I've been going with "examples" pages for e.g. Factorial, Euler Phi Function, and so on, and that seems to work. I thought it was a good idea here because it is truly such an arbitrary instance of an application of the technique. There is probably no direct application of it in practice, unless it turns out to be crucial in the calculation of the efficiency of some algorithm somewhere which Knuth investigates elsewhere in TAOCP.  Hence rather than cluttering up a category with lots of instances of awkwardly-named applications of a specific general rule, the use of "examples" could be the way to go.  And such a page would end up being that aggregation page which you suggest -- and we would go down that route, separating off the given example into a subpage, as and when we get more examples. --prime mover (talk) 04:29, 27 August 2016 (EDT)


 * I see where you're coming from there, and in general I agree. E.g. $10!$ is an undisputed example of the factorial. But in this particular case it looked more like an arbitrary application. Oh, you also wrote that. But the problem I see here is that the example can be proved in its own right, without reference to what it purports to be an exampel of, voiding its status as "example".


 * But then maybe the scope needs to be widened, and the question raised whether this very arbitrary result (the example) ought to be on at all.


 * This all irrespective of the fact that I don't mind categories filled with slightly awkwardly named pages. After all, the results are also obscure and awkward. We might need a category Category:Floor and Ceiling Identities which serves exactly the purpose of containing the strange names.


 * My main objection is that the result is not an "example" in the direct sense. That would be just picking $m,n$ and showing what happens. Therefore, we shouldn't name it as such. &mdash; Lord_Farin (talk) 12:37, 28 August 2016 (EDT)


 * "... the question raised whether this very arbitrary result (the example) ought to be on at all." This question was raised back as long ago as 2008 or 2009 where someone asked for examples, exercises, specific instances, and so on. At the time we said: yes, if anyone can be bothered to put them up, but the people raising the suggestions of what ought to be on  never actually did any of the work to make it happen. Usual thing, bit like working in the industrial / commercial / financial sector really. I'm used to it.


 * But I contend that it is an example of an "example", because it is deliberately contrived so as to illustrate how this sort of problem is solved by noticing that it can quickly be manipulated into the form where the result can be used. I can see your point of view, because I thought about it and considered it, but (at least for this particular example) I think the approach I picked is better.


 * But I'm not too worried either way, except that I do believe the result should stay on . A healthy library of examples of uses of the results is something that lots of people have requested. The only barrier to this is the motivation to post them up.


 * Feel free to move it around, rename, restructure how this sort of thing is held in the database etc., no worries. --prime mover (talk) 15:18, 28 August 2016 (EDT)

With that rationale, I guess I can live with it. At least for now. Let us carry on. &mdash; Lord_Farin (talk) 00:09, 29 August 2016 (EDT)


 * ... although recent contributions make me uneasy about having started this trend. --prime mover (talk) 01:00, 29 August 2016 (EDT)

divides
On my screen at least, $n \divides m$ shows a diagonal line from top left to bottom right. This seems wrong to me. I have always seen the divides symbol as a vertical line, generated by \mid in latex. I do not know where the \divides command comes from. Robsiegen (talk) 02:42, 11 September 2018 (EDT)


 * See Definition:Divisor (Algebra)/Notation --prime mover (talk) 02:59, 11 September 2018 (EDT)