User talk:Prime.mover/Archive 2

This is an article of past discussions, from 13-June-2011 to 26-Nov-2011. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

sin(x)/x

Thanks a lot! I'm only a college student but I know some proofs, I'll see what I feel like contributing :) --GFauxPas 14:47, 23 September 2011 (CDT)

Tidy up

My talk page was getting a bit long so I've purged it back - removed a lot of old stuff which is no longer relevant, and some phatic talk. Don't be offended if I've deleted your comments. --prime mover 00:26, 13 June 2011 (CDT)

Thanks for help "Prime.mover" yesterday I was wondering about the signature and how to put it at the end of my talk but really I dont know how !! I try to search but I dont know how ! thanks for helping me and for this information.--Noor 17:03, 13 June 2011 (CDT)

Notation

I understand the desire to promote unconventional notation--I would love to replace every $2\pi$ with $\tau$--however, conventional mathematical notation is very important to the culture of mathematics. Long standing traditions, like $\pi$, give insight to the often overlooked human history of the subject.

Contributing to any wiki project naturally implies a collaborative effort, as you state in the caveat. However, I do not believe that this ought to be interpreted as a license to use other people's contributions to promote one persons campaign for a revision of the mathematical language. Conventional mathematical notation emerges through a natural selection process--not by force. With all due respect, I believe it is in the spirit of such a project for everything (including house style) to be open to debate.

When it comes to the different symbols for divides, the conventional notation deserves a chance. Surely I am not the first person to post work containing the $\mid$ symbol for divides. I propose allowing both notations to appear, perhaps with a link to a page for public debate.

--TruXus 21:45, 23 August 2011 (CDT)

Yes, indeed this is one of those things I consider important--my inner math nerd can be quite passionate. Thanks for being flexible, I'll try to not be much more of a nuisance.

Btw, I should say that I really love this project and am very happy I came across it. I've been telling all my friends about it. --TruXus 00:48, 24 August 2011 (CDT)

Milestone

I should be able to keep an eye on it. I'm traveling tomorrow night, but worst case scenario I can count backwards and figure out which was number 4000. --Alec (talk) 17:45, 24 August 2011 (CDT)

I'm out of Internet range for the next three days, so I can't watch the proof count. All yours til I get back. --Alec

Set Theory - "Long-term" Goal

You may have noticed that I've been writing up a lot of proofs from the book "Set Theory and Its Logic" My semi-short term goal with this is to create a formalization of natural numbers and natural number arithmetic using a single definition (not these joint recursive definitions involving the successor function). However, before I do this, I need add a few theorems on some set theory, then construct a recursive template (which could be useful in other ways, too) from which I will define addition, multiplication, and exponentiation in natural numbers. This fills the gap between set theory and arithmetic, and it's very useful. It's an alternate formalization of natural numbers (the formalization itself is not quite as useful as that of natural numbers off of ordinals, because it doesn't come in with a built-in ordering relation that remains true for higher cardinals, but it's significantly easier because it's not necessary to deal with Limit Ordinals. Plus, it's something I've never tried before, so I'm hoping to learn something along the way). -Andrew Salmon 02:01, 13 September 2011 (CDT)

It's actually possible (as is done in Set Theory and Its Logic) to define natural numbers and addition, multiplication, and exponentiation by a direct definition instead of a self-referencing recursive one. This is what I plan to do - but there is a specific term Quine uses as a recursive set generator and and a definition for iteration of a function a certain number of times. What should I call these definitions, which are used mostly for construction of natural numbers and definition of addition, but it's used just enough to be essential. -Andrew Salmon 18:57, 13 September 2011 (CDT)

Use the specific term that Quine uses. Can always be changed if there's a better one. --prime mover 00:16, 14 September 2011 (CDT)

Changing name of proof

Could you tell me how to change the name of a proof page once you have created it.Cause you asked me to change the name of

my proof Fifth Postulate but since I'm a newbie to the site, I don't know how. Could you help me?

P.S. I am from Kerala,My mistake earlier.

- Sreeteen

Axiom schemes for predicate calculus

Hi, do we already have axiom schemes for predicate calculus? If not, I can add them and develop some basic theorems. -Andrew Salmon 17:39, 14 September 2011 (CDT)

Look at Category:Predicate Calculus and see that page, that's where it starts from. --prime mover 00:15, 15 September 2011 (CDT)

EDIT - Also, I'm not completely comfortable with the fact that we only have natural deduction axioms so far (I'm used to Hilbert-style axioms). Could I add Hilbert-style axioms for propositional and predicate calculus (then that's all the axioms we need). -Andrew Salmon 23:30, 14 September 2011 (CDT)

Certainly. If there turns out to be a lot of duplication, then, shrug, there will end up being a lot of merging. --prime mover 00:15, 15 September 2011 (CDT)

Greetings

Hi. Just found the site from google, seems really interesting. Was just wondering if it's allowed to add proofs that aren't necessarily theorems like homework proofs? e.g gcd ((a^m)-1 / a-1 , a-1 )= gcd (a-1,m) Ddanndt 15:34, 26 September 2011 (CDT)

If it's a mathematical truth, then there's no reason not to include it. Let's stick it between $\LaTeX$ delimiters and muck about with it:

$\gcd \left({\dfrac {(a^m)-1} {a-1}, a-1}\right) = \gcd (a-1,m)$

... that's one I don't think we've got. Feel free to put it in (but I reserve the right to change its name and tidy it up). --prime mover 16:08, 26 September 2011 (CDT)

Collapsible section

Unexpectedly, I have a rudimentary working version already. It can be found on User:Lord_Farin/SandboxTemplate, and examples of the use can be found at User:Lord_Farin/Sandbox. I plan on making the functionality much like that of the eqn template. Please tell me what you think. --Lord_Farin 15:52, 15 October 2011 (CDT)

Addendum : For it to work, you need to copy the contents of User:Lord_Farin/common.js to your own User:prime.mover/common.js. --Lord_Farin

Awesome! I like it, though I would put "(show)" on the RHS is smaller font and as "[show]', similar how how it has "[edit]" (if you have it enabled in your settings). --Joe (talk) 16:28, 15 October 2011 (CDT)

As well, I think this would be good for all sections in all pages. --Joe (talk) 16:29, 15 October 2011 (CDT)

Hmm ... maybe. I'll get back to you in a day or two - I've been waylaid by the latest Terry Pratchett novel and am unable to do any work here till it's finished. --prime mover 18:09, 15 October 2011 (CDT)

It might be feasible to do something like this (a bit simpler is enough for me, but for a simple idea): [1]. The question is if we want to pay the 17kB load (Yahoo User Interface is used) it brings with every page. --Lord_Farin 18:13, 15 October 2011 (CDT)

Yeeeek! I've had my face shoved far closer to YUI than I ever wanted it in my professional capacity, and my view is that we ought not to if we can do stuff without it.

I also don't like the idea of making all sections foldable. Small pages you just want to be able to see without clicking pesky "show" links, particularly the link at the top. Can we just keep "show" links to pages that need it? Particularly for lemmata, maybe, and only for pages which are currently unwieldy. Pages which already look good I'd rather we left as they are. --prime mover 05:10, 16 October 2011 (CDT)

... sorry - forgot to mention: brilliant job. --prime mover 05:54, 16 October 2011 (CDT)

I'm also not so much a fan of YUI. That said, I like the idea of making sections foldable, not by default folded though. --Joe (talk) 09:01, 16 October 2011 (CDT)

Thanks for the heads up. I agree with prime.mover; this should not be over-used. Furthermore, I dislike the WikiPedia style, which puts the [show] link on the right side of the page, as it is contrary to our short sentence house style.

I propagate the default folding, as otherwise the effect will most likely be lost... Also, please note that disabling JavaScript in your browser will not make items inaccessible; they will never even gain the show/hide link, and visually I think nothing will change. I will try to adapt the template to facilitate larger sections of text to be inserted. --Lord_Farin 02:03, 17 October 2011 (CDT)

That is done. However, it does not yet work with the [edit] buttons on the right. Is there any way I can control which edit page they refer to?

The font of the link can be adapted by using some CSS. I haven't looked into it, but there is a span tag surrounding it, which always has the same class; it shouldn't be too hard. --Lord_Farin 02:28, 17 October 2011 (CDT)

It allows nesting of foldable sections, which is good.

What is less good is that you appear have no control over the level of heading (it appears always to be level 3). I would't know how to fix that, but suggestions:

a) Add a parameter for the level of heading: 2, 3, etc.

b) Default to 2 (as that's the usual default level of "Proof".

c) If the sections are nested, default to one plus the level of the one you're nesting in.

Just suggestions - which may or may not be feasible. --prime mover 06:56, 17 October 2011 (CDT)

I have implemented a) and b). Although I have taken the liberty to default to 3 as this will most likely not be for hiding entire proofs of theorems, but for lemmata. c) is technically hard, if not impossible. The implementation of this appears to have broken the [edit] links for separate paragraphs. That's not bad, as it didn't function properly anyway. --Lord_Farin 07:41, 17 October 2011 (CDT)

I've never been a fan of the mid-page "edit" links anyway, as they cause xtra linebreaks between sections to be lost, resulting in muggins having to get in there to make an edit specially to add the extra linebreak in, so as to space it aesthetically again. --prime mover 10:25, 17 October 2011 (CDT)

If one would allow me access to the MediaWiki:common.js and MediaWiki:common.css files, this template could be up and working by tomorrow. It might want to be positioned in the proofwiki specific editing shortcuts. If this is too early in your opinion, I might develop some appropriate CSS to style the [hide/show] part. --Lord_Farin 16:37, 17 October 2011 (CDT)

Joe is the one who holds the metaphorical purse-strings in this matter ... he's the one who has done most of the work (in fact, all of the work) on the javascript and CSS on this site so far (I lack the patience nowadays, unfortunately). Suggest you get together with him and take it from there. --prime mover 16:50, 17 October 2011 (CDT)

The functionality has been implemented. The templates are Template:begin-foldable and Template:end-foldable. --Lord_Farin 12:49, 18 October 2011 (CDT)

Nice one - I'll come out to play later, once I've sorted out a tottering tower of tomes ... --prime mover 12:55, 18 October 2011 (CDT)

Block determinant

I would say that the result mentioned in Determinant for Block would be a valuable addition to PW. That being said, I agree with your point that I probably had better not given the solution straight away. My enthusiasm sometimes just takes over ;). Thanks for the pull towards reality and purpose. Any chance you can respond to the various talk pages I opened yesterday? I'm still quite reluctant to delete approaches, as I just might be not familiar with them. --Lord_Farin 11:50, 24 October 2011 (CDT)

Yeah I'll get to it, no worries, Mondays are busy.

I agree that Determinant for Block is a good result - but this is the first time an anonymous luser has actually posted up a demand for a result - it's not something I ever envisaged. (It's the wording: "Can you give me ..." not even a bloody "please"!) The page, as I say, can be deleted, and a new page started with the result on it.

Apologies but I just don't like anonymous contributors! --prime mover 12:43, 24 October 2011 (CDT)

PW Style

Is the style as used on Exponential on Real Numbers is Group Isomorphism for multiple proofs the new standard? Before, there used to be a separate section for each different proof. I would recommend the latter as to facilitate a clear distinction with the even smaller subsection headings for eg. lemmata and induction steps (which now, hypothetically, would yield an induction argument for a proof of a lemma, used in one of multiple proofs, to have the unavailable heading 5). --Lord_Farin 14:42, 26 October 2011 (CDT)

If there are multiple proofs, and a proof is complicated and needs several sections, then I would recommend that the proofs go in their own separately-transcluded pages. In that case, the formatting of the headings can be more flexible as you can use onlyinclude to ensure that the headings of the appropriate levels go on whichever pages they are meant to.

With these little theorems and little proofs, I find it makes it look neater to bag all the little proofs into one larger blanket section. It's by means of a sort-of experiment, to make it look sweeter. (Ultimately. every proof would have its own separately transcluded page, but I'm not up for that type of work tonight. My boss asked me to research SharePoint today, and I've come home from work tonight positively brain-damaged.) --prime mover 14:48, 26 October 2011 (CDT)

A bit less important, but nonetheless relevant I think: What is the convention for the placement of $\blacksquare$? That is, which of the forms:

Hence the result.

$\blacksquare$

Hence the result.

$\blacksquare$

...is preferred? I have seen a lot of inconsistency on this part. --Lord_Farin 10:30, 5 November 2011 (CDT)

The first, but as you say it's a bit inconsistent. Not a big issue, but consistency is nice. I also try to put two blank lines before the next section so there's a nice big gap. --prime mover 13:22, 5 November 2011 (CDT)

Another thing. Investigating tableau proofs today (hard to miss those thousands of added characters ;) ) I found that the axiom pages state one should use $\mathrm A$ instead of just A for an assumption. Presumably we are too lazy to enforce the first everywhere we see it, but it is still preferred? --Lord_Farin 12:35, 10 November 2011 (CST)

Don't really think it matters. These were among the first pages I posted to PoofWiki and were basically copypasta from a book I'd been writing. Haven't stopped to give it a thought since. --prime mover 13:33, 10 November 2011 (CST)

Method question

I would like to add a reference to Definition:Integral Domain from Definition:Domain (in italics at the top of the page). Is there a preferred way to do so? --Lord_Farin 16:48, 18 November 2011 (CST)

What, as in "Don't confuse with", or "Also see"? We have it but don't often use it. See Template:About and see its use in Cauchy's Theorem. Have fun. --prime mover 16:54, 18 November 2011 (CST)

Thanks, that's precisely what I meant. I recalled seeing it somewhere. The transition is done; mind though that I haven't got the time to weed through all the pages linking to simply 'domain' and change the reference. --Lord_Farin 03:43, 19 November 2011 (CST)

Better idea: instead of "Domain (Mapping Theory)" make it "Domain (Set Theory)" and make the subpages "Domain (Set Theory)/Mapping" and "Domain (Set Theory)/Relation" with "Domain of Mapping" and "Domain of Relation" as redirects. Thought of it just now while I was out getting my paper. Leave it with me, I'll sort it out later. --prime mover 03:58, 19 November 2011 (CST)

Wolf child?

I'm not quite that young, but I appreciate the estimation. :D (It's probably a closer estimate than the typical one for a Ramsey hypercube problem, though.) TricksterWolf 01:17, 21 November 2011 (CST)

Complexity = Rigorousness???

Why do you think that $\forall C \in \mathcal P \left({\mathcal X}\right) \setminus \left\{{\varnothing}\right\}: d \left({x, \varnothing}\right) > d \left({x, C}\right)$ is more rigorous than $d \left({x, \varnothing}\right) = +\infty$ for all $x$??? --Pantelis Sopasakis 09:56, 26 November 2011 (CST)

Because $\infty$ is a concept which is itself is not rigorously defined. --prime mover 09:58, 26 November 2011 (CST)

Who says so? Can you give a reference that the infinity is not rigorously defined? (in modern math of course). $\infty$ is perfectly rigorously defined - There is even extended-real-valued analysis and calculus on a very rigid theoretical basis. I think it's high time we started including citations under what we post to argue on some reasonable basis. --Pantelis Sopasakis 10:04, 26 November 2011 (CST)

I have been adding citations to all the work I have added to this site, even to the extent of going back through all my source works and adding those citations from where I got them.

I agree that $\infty$ is a convenient piece of notation, but you cannot deny that what I wrote is a mathematically correct definition for the shorthand that is $d(x,\varnothing) = \infty$.

Now, where are your citations??? --prime mover 10:11, 26 November 2011 (CST)

I will take some time later to add citations to what I have already posted. I asked for a citation to a claim of yours that is absurd (that mathematicians have not yet come up with a rigorous definition of the infinity). It is good you add citations but I guess you have some profit from the advertisements on your site. I am doing it just to provide my knowledge (however little it is) to the people. Do you see some difference in the incentives? :-) Have a nice day. --Pantelis Sopasakis 10:22, 26 November 2011 (CST)

This site makes no profits. It is entirely a labour of love. --prime mover 10:26, 26 November 2011 (CST)

Notational Conventions?

I noticed that you like changing the notational conventions I use into different ones, that you like. But in this sense, this is not a Wiki. This is Prime Mover's Site that he needs some help from other people to populate it with math... At least create somewhere a page and put it straight. $2^X$ denoted the powerset and especially when it is written explicitly and with a link to the definition of the powerset on this wiki, why should you change it?

House style. It's what the site started with. It makes sense to keep it consistent. Most other contributors are prepared to accept the house style (which has evolved over the years).

But to a certain extent you're probably right. So I didn't actually set the site up, but approximately 90% of the content has been provided by me. --prime mover 10:07, 26 November 2011 (CST)

Anyway, if you want to run your own site, create a blog. Wikis are not supposed to have owners - they are public. And if you want my opinion, if you want this thing to go anywhere you need people's contribution... --Pantelis Sopasakis 10:16, 26 November 2011 (CST)

One more thing: Let's put an end to this discussion and do sth more useful... Add some theorems on the site for example (and not edit each others notation). --Pantelis Sopasakis 10:17, 26 November 2011 (CST)

This site is what it is. It can be described however you like. Please note the caveat at the bottom of the edit page: "If you do not want your writing to be edited mercilessly and redistributed at will, then do not submit it here." (My emphasis.)

The house rules are what they are, and have been contributed to by more than one person, so it's not all just me. The same applies to Wikipedia - if you were to add content which was contrary to the rules, it would soon be deleted. On this site you are at least offered the courtesy that your work remains in place - just using different notation. If you are unhappy with this to the extent that you can not compromise, then we can come to an arrangement whereby your notation remains as you prefer it.

Your contributions, as I said earlier, are welcome. Feel free to keep adding them. I will refrain from changing your notation. However, I (and other colleagues, when they're on line, they probably have lives) reserve the right to edit other aspects of your contributions (e.g. their overall structure) as appropriate to confirm to the site's general philosophy. --prime mover 10:25, 26 November 2011 (CST)

Introduction of Notation

In a way, I want to introduce a notation for things like "$\prec$ is a strictly well-founded relation as it is done in the literature, because it makes the substitutions clearer. What would you suggest as formatting? Also, how do you create a signature again? --asalmon

I confess I haven't seen what's done in the literature, so I confess to being out of touch with it. If you mean "how to format $Fr$" for example, then use $\operatorname{Fr}$ which then identifies "Fr" as being an operator. It may seem like a tedious lot to type, but you can set up a template in your pages and use cut-and-paste.

Note that when you invoke the notation, you are advised to add an explanatory "where $\operatorname{Fr}$ denotes that (blah)" and link to the appropriate page. Saves me doing it - I'm on domestic duty today. --prime mover 11:43, 26 November 2011 (CST)

Creation of a "Properties" page

I have created various pages on the Inner limit. I think it is expedient to create a page titled Properties of the Inner Limit for reference which will compile a list of the main facts regarding the inner limit with link to individual pages. What do you think? --Pantelis Sopasakis 11:37, 26 November 2011 (CST)

If you like. See Subset Equivalences and Trigonometric Identities for examples. Alternatively (or additionally), set up a category for Inner Limit (see the various subcategories off, for example, the Topology category). --prime mover 11:39, 26 November 2011 (CST)

Question on Notation: $\epsilon$ vs. $\varepsilon$

When should we use the simple greek characters like $\theta,\epsilon,\phi$ ($\theta,\epsilon,\phi$) and when the characters $\vartheta,\varepsilon,\varphi$ ($\vartheta,\varepsilon,\varphi$)? Is there a page where one should post questions on notation? --Pantelis Sopasakis 11:48, 26 November 2011 (CST)

I've never seen the point in using the variants, it's more to type and they're ugly. Some prefer $\vartheta$ for a topology, some prefer $\tau$ (depending on who you read). As for $\varepsilon$ I've never seen the point to it. If you really prefer the clumsy versions, I'll leave them alone. --prime mover 11:51, 26 November 2011 (CST)