Talk:Cosine of Sum

Domain

The domain is never specified. If the domain is $\R$, then the first proof which invokes complex numbers is invalid. If the domain is $\C$, then it is next to impossible to identify the real parts, since $\cos a$ might be complex. --kc_kennylau (talk) 11:51, 28 October 2016 (EDT)

I accept your point about the complex case, but why is the proof invalid if the domain is real? --prime mover (talk) 14:31, 28 October 2016 (EDT)

I take back my point. The domain is $\R$ then. --kc_kennylau (talk) 20:03, 28 October 2016 (EDT)

So, all proofs except the third one apply only to $\R$. Should I tag it as refactor? --kc_kennylau (talk) 08:24, 29 October 2016 (EDT)

I'm not sure how this would have to look like. After all, we want the result to be easily accessible, but also the proofs properly structured. Perhaps subpages for Real and Complex cases in the way we've done much more often (I can't come up with an example off the top of my head). — Lord_Farin (talk) 11:18, 30 October 2016 (EDT)

I can't immediately think of a better way of attacking this problem than the way kc_kennylau is currently doing it. That is, each page with a statement on it that can apply to different domains is split into two subpages: one for the real result and one for the complex one. They can then be put onto separate pages and transcluded. If for any pages this leads to unnecessarily duplication (because the proofs themselves are identical but for the domain they are in), we can think of a way to resolve this at that point.

But for the moment, I believe our best approach is "dive in, we will test the temperature of the water later." --prime mover (talk) 11:24, 30 October 2016 (EDT)

Maybe we can take an intelligent approach and start with the theorems where the proofs do not match.

It's tricky because we need to keep in mind that we're doing this only (or: mainly) for the people unfamiliar with complex analysis (i.e. those who cannot discern when a proof for $\C$ can mutatis mutandis also work for $\R$) while for another segment of the readers, the separation is completely artificial.

Thought should be put into the presentation of this. I would be inclined to not duplicate proofs, because it is indicative of a better solution waiting just around the corner. — Lord_Farin (talk) 11:33, 30 October 2016 (EDT)

What should be the subtitles (e.g. "Proof 1" or "Proof for Real Numbers")? --kc_kennylau (talk) 11:43, 30 October 2016 (EDT)

More like "Cosine of Sum/Real/Proof 1" and the like. So with a proper intermediary set of pages which look like this one currently does, and then an overarching "Cosine of Sum" page which serves as a search engine target. — Lord_Farin (talk) 12:09, 30 October 2016 (EDT)

Gosh, that is a lot of refactoring. --kc_kennylau (talk) 12:15, 30 October 2016 (EDT)

I guess you found the reason why we managed to accumulate a backlog of 700+ pages in the Refactoring category. — Lord_Farin (talk) 12:22, 30 October 2016 (EDT)

Can I just change one word in Derivative of Composite Function? --kc_kennylau (talk) 12:34, 30 October 2016 (EDT)

Is it /Corollary/Real or /Real/Corollary? --kc_kennylau (talk) 12:40, 30 October 2016 (EDT)

Neither. --prime mover (talk) 12:55, 30 October 2016 (EDT)