Definition talk:Pointwise Operation/Real-Valued Functions

Maybe Category:Pointwise Operations is justified (with corresponding Definitions category). --Lord_Farin 07:36, 6 April 2012 (EDT)

I'm trying to add a link to what "operand" means but I can't figure out how to link to a subpage of a subpage of a page, Definition:Operation. How do you do that? --GFauxPas 08:18, 6 April 2012 (EDT)


 * You can use a sharp sign (#) (more commonly known as 'hash sign', but I'm a bit recalcitrant). That would make Definition:Operation. But maybe Definition:Operand could be redirected there. --Lord_Farin 08:22, 6 April 2012 (EDT)


 * A $\sharp$ sign is technically a different beast from a $\#$ sign. Horizontals, not verticals, are oblique. --prime mover 10:09, 6 April 2012 (EDT)


 * I should have been more careful in my recalcitrance and have written octothorpe instead. --Lord_Farin 10:26, 6 April 2012 (EDT)


 * Okay, so that's already in place. --Lord_Farin 08:22, 6 April 2012 (EDT)


 * Oh whoops, thought subpage of a subpage would be different than just subpage. --GFauxPas 08:35, 6 April 2012 (EDT)


 * While I think about it, I am not keen on using links with # in them. I would rather that a redirect were used to point to that page, and then that redirect used exclusively. (The reason is, if we then decided to refactor, and take that section out and put it into its own page, the amount of rework needed on pages which include that # sign in the link will be minimal.) You-all may have seen me changing such links with # in them so as to use those redirects. Like a fool, I sort of expected this to be picked up on and copied. Never mind, I live and learn. --prime mover 10:09, 6 April 2012 (EDT)
 * Oh I did pick up on it, but I usually don't take the effort to see if there's a redirect to the page I want to link to. I also just thought it was just "prime mover's thing" and that there wasn't a reason for it. --GFauxPas 10:32, 6 April 2012 (EDT)

Page name
The way I suggested this working when this was first discussed was for this to be a subpage of Definition:Operation Induced on Set of Mappings. The reason for this was so that it could be easily transcluded, in that there is an immediate link back to the parent page so as to emphasise the link between them.

However, I wonder about the need for transclusion, given that there is a link from one to the other which works perfectly well - so suggest (as that is what is being used already) that this page is in fact renamed directly to Definition:Pointwise Operation on Real-Valued Functions. Then this page could probably be disposed of. Thoughts? --prime mover 10:09, 6 April 2012 (EDT)


 * In constructing this page, I chose to avoid transclusion of it onto the 'main' page as it is completely self-contained, and an instance rather than a sub-definition. That is, I agree. --Lord_Farin 10:26, 6 April 2012 (EDT)


 * Moved as suggested. Good job. --prime mover 11:48, 6 April 2012 (EDT)

Another structural rethink
I'm having further thoughts about how to structure this area of the wiki. We are in danger of repeating ourselves all over the place at the moment, which would be inefficient and fragmentary. In effect we have one basic concept: "pointwise operation" which is $(f \oplus g)(x) = f(x) \oplus g(x)$ where $\oplus$ is any Definition:Binary Operation defined on $\operatorname{Cdm}(f)$ and $\operatorname{Cdm}(g)$.

(Yes, this itself is a specific instance of a general Definition:N-Ary Operation on the Definition:Codomain, and this also needs to be taken into account, but let's not run before we have demonstrated the ability to walk.)

The specific instance of $\oplus$ being $+$ and $\times$, and of the codomain being $\R$ or $\C$ or whatever other standard number set, could / should then be transcluded as instances of that basic definition, in the same way as (for example) Definition:Addition is in the process of being configured (work in progress, piecemeal).

The current structure of this page makes it difficult to see where the definition in one context finishes and the next context starts.

I will give this area of activity some more thought, and possibly start working on it. An instance of what I think is the base definition for this page is as in Definition:Pointwise Operation on Complex-Valued Functions, which itself would be transcluded into a general page Definition:Pointwise Operation on Number-Valued Functions or some such. --prime mover (talk) 10:50, 6 October 2012 (UTC)


 * Yes, it appears that the def for $\C$-val fns is clearer, cleaner and more efficient. The subpage/transclusion mechanic has done an excellent job in the past, and I think it can have equal merit here. Please do continue. --Lord_Farin (talk) 10:55, 6 October 2012 (UTC)