User talk:Abcxyz

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 * --Your friendly ProofWiki WelcomeBot 18:10, 2 March 2012 (EST)

Amending existing pages
What I've seen you've done is taken existing pages and rewritten them. In particular you have expanded the context of a lot of pages so as to include the complex case. While this in itself is no bad thing, I have concerns about how (in particular) the Definition:Radius of Convergence page has been completely changed.

The philosophy of this site is to include definitions for all the various contexts into which they are encountered. So we would include this definition for both real and complex numbers - and the same applies to all the other definitions that you have amended to make more general.

I admit that complex analysis has not been addressed properly yet - that is purely due to me (or anyone else) not having got round to plugging away at putting the foundations in place. As you will have noticed, another philosophy of this site is to ensure that the foundations of a subject are put in place as rigorously as possible first.

In short, please don't change the context of existing pages (in this particular case from the real to the complex domain), instead add a separate definition for the extended definition. Otherwise people coming to this site to use it as a resource who don't understand complex numbers will not be served well.

I will go through and see if I can sort out what you've already done (I hate to use rollback indiscriminately, so I'll see if I can find the time to invest to sort it out properly), but in the meantime please bear in mind what I put here. --prime mover 01:17, 7 March 2012 (EST)

links
Please do not include the underscores in links on pages. That is, not like this:
 * Derivative_of_Complex_Power_Series/Proof_2

Like this:
 * Derivative of Complex Power Series/Proof 2

Otherwise maintenance becomes a nightmare. --prime mover 01:28, 8 March 2012 (EST)

Minor point
I see you are going through the foundations of complex analysis. There is one tiny issue that you might have glanced over:

In house style, we have brackets inside left/right delimiters in TeX, like this:

$\left({parentheses}\right)$

instead of

$\left( parentheses \right)$

They help to distinguish the left and rights, and are effectively enforcing the bracket matching (because TeX needs to close every opening brace to work). Otherwise, keep going! --Lord_Farin 11:07, 9 March 2012 (EST)


 * Concerning Combination Theorem for Continuous Functions/Sum Rule, you were restricting the result statement. Also see the Talk page I just started. --Lord_Farin 12:41, 9 March 2012 (EST)

More comments on Complex Analysis proofs
You ae still working on extending the scope of some of the Real Analysis proofs to take on Complex numbers, but you are doing this by just changing the $\R$ to a $\C$ (and doing some minor rewording). While I appreciate that some of those proofs themselves are the same for $\C$ as they are for $\R$, we do not want to remove the "real analysis" versions of these proofs. As has been pointed out before, it is important to keep the "real only" proofs because many of those who come to this site have not studied complex analysis.

Besides, this is a repository for proofs, not just results. If there are 16 proofs for a given result, we give them all.

What this means is that the real-analysis version of the proof (and the statement) is equally valid.

Why? you may ask. Because no other site does.

And there's more. Some of the proofs apply to $\Q, \R, \C$ but not to $\Z$ (for however obvious the reasons). If we were to bag everything up and say "It's valid for $\C$, that's all we need to know" we lose the subtlety that the result applies also to $\Q$, and thereby is relevant to Diophantine analysis.

Your input is appreciated, but please bear this in mind. --prime mover 13:45, 9 March 2012 (EST)

Nuggets of information
While it's tempting to drop interesting little nuggets of information into pages with headings like "Remark" or "Note" or "Comment" or such like, the trend on this site has been away from this tendency, preferring instead to back up all such statements with a separate page where such a statement is proved or demonstrated, and providing a link to that page in an "Also see" section.

There is a deliberate decision to ensure that ProofWiki is "not Wikipedia" and as such is not intended to be used as an encyclopedia. A definition page is just a definition page. A proof page contains just a proof. The only exceptions are historical notes and linguistic notes, both of which are usually poorly served on other resources.

The vital point above is "providing a link". ProofWiki is far more rigorously linked than Wikipedia, for example, and in fact to a certain extent prides itself on what would be referred to as "overlinking" in Wikipedia. It is this which makes ProofWiki unique and vital. As such, categories are also vitally important, and so is careful naming and equally careful crafting of the LaTeX. --prime mover 17:21, 12 March 2012 (EDT)