Definition talk:Pointwise Operation/Real-Valued Functions

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 of Mapping, 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)

As always, you display admirable perseverance where I would have been overwhelmed by overseeing the huge piles of work. PW would be lost without you. --Lord_Farin (talk) 21:47, 6 October 2012 (UTC)