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)


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


Like this:

Derivative of Complex Power Series/Proof 2#Lemma

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:


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 Sum Rule for Continuous Functions, 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)


I'm not that good at transgomofying pages myself, but take a look at this page for an example of transporation: Equivalence of Definitions of Exponential Function.

You add: {{:Name of Page you want to transqualify}} and that pulls in the "only included" parts of the pages to be transvorfied.

In the pages to be transwaloted, the part that is only included is included is

 < onlyinclude >stuff to be transpoloted< /onlyinclude >

--GFauxPas 22:49, 15 March 2012 (EDT)

What are transgomofying, transporation, transqualifying, transwaloting, and transpoloting? Abcxyz 01:10, 16 March 2012 (EDT)

The word is, for better or worse, "transclude". GIYF. --prime mover 02:50, 16 March 2012 (EDT)

page name changes

I note that you recently changed some of the page names to replace a standard hyphen with some big arse mofo which you can't render conveniently by typing on a keyboard. Just because this is the way twittipedia does it is no reason for us to go down that same pointless route. I have reverted those changes as they are of no worth at all.

Please note that a style has evolved on this website over the last few years. If you see a certain stylistic commonality to the work on here which you object to, then feel free to raise that subject in the main discussion page, so it can be talked over before going in with a program of changes. --prime mover 02:55, 16 March 2012 (EDT)


Thank you for the links to the reading material; it appears very interesting. Unfortunately, I have other stuff to do. --Lord_Farin 07:17, 12 April 2012 (EDT)

Please don't completely rewrite stuff

I understand what you're trying to do (I think): that is, you got your Gaisi Takeuti, which structures stuff in a way which is different from the way Devlin does it. But rather than completely restructure the whole way the Devlin work has been reported, it is always better to provide second proofs. It's take me longer than I wanted to to work out where the "Ordinals are Totally Ordered" page came from, and it turns out it was ripped from Relation between Unequal Ordinals. Now to my mind the fact that ordinals are totally ordered follows from Relation between Unequal Ordinals - but what we now have is that Ordinals are Totally Ordered --> Ordinal Membership is Trichotomy --> Relation between Unequal Ordinals which seems to be going in the wrong order.

When you approach a topic from a different direction, please respect any existing work and include your work as an addition to what's already there, not instead of. Otherwise you may be in danger of your work being reverted, which will be a shame as that means you're wasted your time as well as mine. --prime mover 06:21, 28 June 2012 (UTC)

Sorry for anything I have messed up on; I have simply tried to present the proofs in a more concise manner and I never intended to replace existing work with my own. From your note, I guess I might have done it unintentionally and don't always make the best decisions.
I'm not sure what you mean by the "wrong order". I just felt that it was more natural to present Relation between Unequal Ordinals as a consequence of Ordinals are Totally Ordered; that way, there wouldn't be the invocation of Ordinal Subset of Ordinal is Initial Segment at both the beginning and the end of the proof. Those pages are linked to by only a few pages anyway. But if you think it is better your way, I won't try to change it to another way. --abcxyz 06:44, 28 June 2012 (UTC)
With linking to the appropriate proof subpages of these theorems it is technically (in the true sense of the word) possible to let you both have your ways; this seems to me like a good solution. --Lord_Farin 06:54, 28 June 2012 (UTC)

house style

I trust that you have read the style guide?

The idea of ProofWiki is that a carefully annotated and fully-amplified proof is provided to as great an extent as possible. It is completely contrary to our philosophy to reduce it all down to one line and remove all links as to the reason for it. What was the reasoning behind the recent spate of edits to Union from Synthetic Basis is Topology? --prime mover (talk) 21:11, 25 September 2012 (UTC)

Edits to topological pages

I see you're generally going through and changing the symbol used to define the topology in a topological space (e.g on Definition:Product Topology from $\vartheta$ to $\mathcal T$). Please don't. We already have too many of these: various contributors have brought their own favourites to the picnic and so we have at least $\vartheta$ and $\tau$ being used - arbitrarily changing them to your own personal favourite is not on. We are aiming for a consistent style. --prime mover (talk) 05:35, 7 October 2012 (UTC)

... although having studied that particular page I can see what your aim was so I can see where you were coming from - still, while $\mathcal T$ is used (here) to denote the product topology, the individual factor topologies are IMO best left with the standard symbol(s) for a topology that have emerged on this site. --prime mover (talk) 06:10, 7 October 2012 (UTC)
Okay, thanks for your comments. I'll keep them in mind. --abcxyz (talk) 14:06, 7 October 2012 (UTC)


You will understand why I got short with you. You made a change to what I wrote, claimed it was my grammar that was at fault and then replaced it with an egregious grammatical howler of your own: "... it does not necessarily follow that ..." which it may educate you to re-read.

What you had in fact noticed that there was a mathematical error I had made: it was not the mapping that was compact but the metric space it was a mapping from. If you had not accused me of having written something ungrammatical I would have looked closer at it, and perhaps been marginally more polite. --prime mover (talk) 21:55, 4 November 2012 (UTC)

I didn't look at all the revisions and see if you wrote it or not. I didn't assume that you wrote it (in fact I didn't know that).
Well, yes I did assume that it was a misplaced modifier, and it didn't occur to me that it could have been a mathematical mistake instead. Sorry for the confusion.
Also, I hope you didn't take it the wrong way when I called the "Warning" section "stupid". I just don't understand how anyone, on a normal day, could ever confuse the statement "$f$ is uniformly continuous $\implies M_1$ is compact" with the Heine–Cantor theorem.
--abcxyz (talk) 22:16, 4 November 2012 (UTC)
That's not the point. Heine-Cantor says "Compact implies Uniformly Continuous" (which, loosely, was what the original title was before its author learned that the result had a name). The warning says "Uniformly Continuous does not imply Compact". There are similar sections like this scattered throughout the site, which are gradually being replaced with "also see" sections with links to the page detailing the info in that section. Fact is, I can't do everything at once and I am working through it all bit by bit. If you suggest deleting a section and can back it up with a logical argument, then the response may be positive. Dropping suggestions without explaining your reasoning is not likely to get such a response, because the person putting the page together probably had good reasons of his own to structure it the way he did, and needs a counterargument to do it a different way (which often has knock-on effects which cause a lot of tedious extra work). In particular, if a section is up for refactoring or generally rewriting, quibbling over perceived grammatical mistakes is pointless because such mistakes will probably be caught and corrected when the rework happens anyway. --prime mover (talk) 23:07, 4 November 2012 (UTC)
Okay, I think I get what you're saying. I'll keep it in mind. --abcxyz (talk) 00:25, 5 November 2012 (UTC)


When you do a refactoring job, like splitting a page into two proofs, please put a note in the "sources" section for the sources to be reviewed. As it is the "Union from Synthetic Basis is Topology" page needs to be so adjusted. If you don't care about sources, no worries - but there is a specific exercise under way (which you may have noted) which is proving surprisingly difficult to do properly. To have an indication that the "flow" of the source works has been compromised would be helpful. --prime mover (talk) 07:11, 20 November 2012 (UTC)

Sorry, I didn't understand that at all. Could you please try explaining again? --abcxyz (talk) 15:40, 20 November 2012 (UTC)
When you created the page Union from Synthetic Basis is Topology/Proof 1 you copied it complete with sources.
When you press the "previous" and "next" field on a source, it takes you to the page in ProofWiki containing the material in the previous/next section of that source work. This is, by design and rigorous application, a linear ordering.
So when you copy the page, complete with sources, that linear ordering suddenly becomes not-a-linear-ordering-any-more and needs work to amend the source links so that it is.
Usually that means that sources which specifically include one of the proofs on that page will have the source citation moved into that page. Pages linking to that page on that aforedescribed linear list then need to be amended so as to point to "blah/Proof 1" rather than just "blah". Into that category goes the source referencing the Sutherland work on the page in question.
If a source, on the other hand, does not actually give a proof, then a link to the main page from which the proofs are given as subproofs is adequate, so those sources stay where they are. Into this category goes the source referencing the Steen and Seebach work on the page in question.
Therefore, whenever a refactoring job is done on a page which includes citations in the "Sources" section, it is a good idea to add a "WIP" or "Refactor" tag or something (doesn't matter what-all) so as to give an indication to one of the team on maintenance duty that this needs to be done. Otherwise it is easy to miss them, and then the exercise of paging through a particular text book becomes that much less straightforward - because the flow is no longer linear. --prime mover (talk) 20:31, 20 November 2012 (UTC)
Thanks, that was much clearer. I understand now. --abcxyz (talk) 21:08, 20 November 2012 (UTC)

delete tabs

When you add a delete flag to a redirect, please don't just delete the content and replace it with that delete flag, even when it is just a talk page redirect.

This has been discussed before on another thread: when there's been a lot of moving stuff around from one page to another, the task of making sure the talk matches up with its material can be missed - specially when a page has been split into several parts and the talk has migrated with it. (Not saying that happened in this case, but that's not the point.) Sometimes the redirect is the only way to work out where the talk came from.

So if you add a delete tag, even though it seems clear to you that a page has no use, leave the opportunity for others to see whether the deletion is necessary or not. --prime mover (talk) 09:40, 25 November 2012 (UTC)

It is the case though that a delete flag destroys the redirect functionality. In such cases, it is perhaps best to add a bit of text along the lines of "(Part of) The discussion previously here pertains to 'page' and so is moved to 'talk page'." rather than to have the redirect. --Lord_Farin (talk) 11:10, 25 November 2012 (UTC)
But when you then go to edit the page to look at it, you automatically see the redirect. Does it still destroy the redirect function if you put it after the redirect? Adding a line of explanation seems like unnecessary work to me. --prime mover (talk) 12:56, 25 November 2012 (UTC)
All right, understood. --abcxyz (talk) 22:02, 25 November 2012 (UTC)

Proofread request

Since you were the one who put up the original version of Compact Subspace of Linearly Ordered Space, I'd appreciate if you'd check it and its lemma over for accuracy. As noted in Subset of Linearly Ordered Space which is Order-Complete and Closed but not Compact, the original version was not correct. Lord_Farin and I came up with an alternative that seems to work. He also has some other related ideas going in his sandbox. Also: the current proof of the forward implication is fugly, using a lemma that feels like it can probably be folded in. Lord_Farin has another (not-quite-complete) proof of that lemma in his sandbox. Maybe you'll have a better way to do that whole thing. Finally, I am curious whether it's possible to do without BPI in the reverse implication (if so, the proof will need a very different structure). Maybe you'll have an idea. --Dfeuer (talk) 20:02, 10 February 2013 (UTC)

Extended absence

Is there any way you could be convinced to come back and finish the amazing work you were doing on defining the real numbers? --Dfeuer (talk) 02:52, 20 February 2013 (UTC)

I think I'll get back in about a week. I will try to finish it. --abcxyz (talk) 18:37, 7 March 2013 (UTC)
That (and further contributions of course) will be greatly appreciated by all. Or at least by me. --Dfeuer (talk) 18:40, 7 March 2013 (UTC)
The nagmail paradigm, incidentally, is a new departure for $\mathsf{Pr} \infty \mathsf{fWiki}$. Is it worth writing a bot, do you think, to automatically send an email (or, in extreme cases of absence) a series of emails with ever more urgent and important sounding messages, along the lines: "You have not contributed in (n) days! Your presence is demanded! You MUST log into $\mathsf{Pr} \infty \mathsf{fWiki}$ and complete your work, or your internet privileges will be terminated indefinitely!
Worth a poke, do you think? --prime mover (talk) 18:44, 7 March 2013 (UTC)
Talk page questions are a sufficient way to handle this, I think. As long as there is nobody noticing the absence there should be no problem taking (n) days off, or that's my view (though I'm pretty sure I'll get notes at $n \ge 3$ already). — Lord_Farin (talk) 22:13, 7 March 2013 (UTC)