User talk:Dan Nessett

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 * --Your friendly ProofWiki WelcomeBot 13:40, 6 March 2012 (EST)

Style pointers
Now there's some stuff there to comment on, there are a few items which you might want to take on board:

a) Use dollar signs rather than "less-than math greater-than" as math delimiters (or anything else). There are good reasons for this: the main ones being 1. it's quicker to type, 2. "math" style delimiters don't get rendered properly in transclusion pages.

b) One sentence / statement / idea per line. This may sound silly, and very few people coming to ProofWiki can get their heads round this to start with. But it makes it easier to follow the proof.

c) Display equations are left-justified but indented, rather than centralised. (This is because the shortness of lines draws the eye to the left.) To indent, start a line with a colon. More colons = more indent, which is what the convention is on talk pages.

d) Lots of stuff is in displaystyle. Even inline code is better in displaystyle. So integrals, fractions, summations, all the stuff which has a compressed format inline, is made to be displaystyle.

e) Anything in parenthesis needs a \left({ and a }\right) round them. Yes I know it's fiddly and many consider it unnecessary. But a) it makes for consistency of style, b) it's an instant check to ensure your parentheses are balanced, and c) when cutting and pasting, and putting something big where once was something small, the brackets will automatically be sized as appropriate. And it's worth making the reminder that use of \big, \Big, \Bigg etc. is completely unnecessary because \left and \right automatically size everything properly.

But all that is documented in the house rules: Help:Editing/House Style. There's loads of stuff.

As for copyrights - couldn't give a damn, myself, but I understand that others feel the need to respect them, so if there is a requirement to add a citation to the page being copied, then such a citation would need to be added to the page, and (as has happened so far) a template would need to be generated. (For a good example of where this was shown to be needed, look up Urysohn's Lemma.) I never bother to cite a reference to wikipedia a) because the latter is too transitory and b) because very little stuff comes from there anyway. I know little about Citizendium except that I believe it "works a bit like wikipedia". As I said earlier, if there is a need to add a citation to work which came from there and that Citizendium owns the copyright on, then give me a link to it and I'll sort out a template. --prime mover 16:20, 8 March 2012 (EST)


 * Thanks for the helpful comments. One question though:


 * The theory pages and proofs had equations that were indented. I removed these because I have a 30' screen and all of the equations appeared in the center, which looked weird. However, from your comments above, it seems you want indented equations, so I can revert to the imported text and work from it. I would like to decide on which is the correct revision to work on before proceeding with further editing, so I don't waste editing effort. Perhaps you would be willing to take look at the original and latest revisions of one of the pages (say, User:Dan Nessett/Sandboxes/Sandbox 1) and let me know which contains the correct markup. Dan Nessett 17:49, 8 March 2012 (EST)


 * It appears that  :$$math$$  behaves different from  :$math$  essentially (even, the math tags apparently take precendence over the nowiki tags, how inconvenient). The latter indents only as much as the colons at the start of our comments do, but the former centers the equation. The latter is the desired behaviour. I guess it's easiest to take the original and run a replace command on the 'math' and '/math' tags to dollar signs. Concerning some strings of equations, it is a good idea to look at Template:Eqn. Example use is abundant over the whole site, a few 'Random Proof' clicks should suffice. --Lord_Farin 17:58, 8 March 2012 (EST)


 * See a) above: replace all the ...  tags with dollar signs. Under the rendering tool used on this site (MathJax), is deprecated and does not work properly. This is important so do that first.
 * Having done that, see c) above. Put a colon before each line you want indented. You will find that a colon in front of a line written using dollar delimiters for your LaTeX will indent it the way you want.
 * Take a look at some examples of most of the other pages on this site. Use "Random proof", for example, and examine the LaTeX. See how it's done, get a feel for how it's structured, go and do thou likewise. --prime mover 18:01, 8 March 2012 (EST)


 * I have created a Citizendium attribution template ( Template:Citizendium ). It is very simple, but solves the problem. If you want to make it more complicated (e.g., so it handles multiple articles in the same reference), put it into a house style, or change it in some other way - feel free. Dan Nessett 14:26, 9 March 2012 (EST)

I am having trouble using \displaystyle. The parser doesn't appear to recognize it as a command. For example, see the first line in Workspace 1. Can you help me? Dan Nessett 15:27, 12 March 2012 (EDT)
 * I was just about to come your way.
 * I'm not sure why it wouldn't work, but I suspect your \limits might have given it indigestion. It's a command I've never bothered to use myself, it doesn't seem to add anything much.
 * Also note that in order to save time and effort, and incidentally it makes it easier to read, I usually (and the house style endorses it, because I wrote it) remove curlies from around parameters in integral limits and top/bottom of fractions when they are single characters, And $d$ as a differential operator is rendered $\mathrm d$, and needs a space before it. Your integral then:
 * $\displaystyle \int_{-1}^1 x \ \mathrm d x$
 * --prime mover 15:31, 12 March 2012 (EDT)
 * I understand it just doesn't work for you? It does for me. Let me do some research ...--prime mover 15:33, 12 March 2012 (EDT)


 * Any progress on the research? I could simply edit the page according to the other house style rules and not change the display equations (i.e., keep them with dollar delimiters). But, I don't know if that is acceptable. Dan Nessett 00:52, 16 March 2012 (EDT)


 * No, sorry. It seems only to be a problem for you, because when I add that displaystyle field it works fine. What browser are you using?
 * I wouldn't worry. Once it's a proper proofwiki page in our standard style, the problem will probably go away. Does the displaystyle command fail to render on your browser in general, or just on that page? --prime mover 03:25, 16 March 2012 (EDT)

When I look at other proofs, the equations containing displaystyle are bracketed by dollar signs (for example, see Triangle_Inequality_for_Generalized_Sums). This is not how displaystyle use is described on the House Style editing help page. When I added the bracketing dollar signs, the equation displayed properly. So, I suspect others have run into this problem and have solved it silently. Dan Nessett 13:35, 16 March 2012 (EDT)


 * The house style page has been corrected; glad that the problem is solved. --Lord_Farin 15:31, 16 March 2012 (EDT)


 * There was a reason for it to have been put on the help page without the dollar signs - it was causing transclusion to misbehave. It was assumed that the reader, understanding the philosophy behind markup languages, would understand that \displaystyle was a LaTeX command and be up to speed with fact that it needed to be within the dollar sign.
 * Strangely, I added the displaystyle to the equation which had been allegedly causing trouble, and seen it working for me, but then it was reversed out again straight afterwards by the OP. From which I had assumed that the change I had done was inadequate.
 * I will bear in mind that contributors to this site may need more explicit instructions, and try to write the instructions more carefully. My bad. --prime mover 15:48, 16 March 2012 (EDT)

Having problems with Aligned Material
Can someone explain what is the problem with the following aligned equation (see the source for the actual markup):

, which equals $2^{l} \ell!$, when x = 1:

This is the aligned version of:


 * $ \displaystyle \frac{d^{\,l}}{dx^{l}}\left({x^{2}-1}\right)^{l} = [\frac{d^{\,l}}{dx^{l}}\left({x-1}\right)^{l}]\left({x+1}\right)^{l} = l! \left({x+1}\right)^{l}$, which equals $ 2^{l} \ell!$ when x = 1:

I have cut and pasted the components of the aligned equation into an online TeX equation display and they work fine. Dan Nessett 13:56, 21 March 2012 (EDT)


 * The problem arises from the fact that we are dealing with MediaWiki here; the construction using   (a template) relies on the non-occurrence of the double closing brace  }}  in a semantic context (like it occurs multiple times in your example). Also, every instance of such a template should be properly closed by a syntactic occurrence of the double brace. Incorporation of these remarks leads to resolution of your problem:


 * Note that I have added the column labelled 'c' to put your comment into (this is the purpose of the column labelled 'c'). Hopefully, the (subtle) differences in both codes will allow you to figure how to use the eqn template properly. --Lord_Farin 14:08, 21 March 2012 (EDT)


 * Thanks. I probably should have figured that out myself. Dan Nessett 15:06, 21 March 2012 (EDT)


 * Don't worry. It took me three days to figure out what was going wrong with our templates when we migrated to MathJax. --prime mover 15:26, 21 March 2012 (EDT)

Aligned Deductions?
I have a line in one of the proofs I am working on that has multiple deductions. Specifically,


 * The bra is a polynomial of order k, because
 * $ \displaystyle

O\left[\nabla^m P_k\right] = k-m, \quad O\left[w\left({x}\right)\right] = 2m \; \Longrightarrow\; O\left[w\left({x}\right)\, \nabla^m P_k\left({x}\right) \right] = k+m \; \Longrightarrow\; O\left[ \nabla^m  \{w\left({x}\right)\, \nabla^m P_k\left({x}\right)\}\right] = k, $

This would read more clearly if there was an Aligned Deductions template. Does such a template exist? Dan Nessett 14:17, 22 March 2012 (EDT)
 * The eqn template should see you right. --prime mover 14:19, 22 March 2012 (EDT)


 * Sorry, but I am not sure how to use the eqn template for this purpose. The most obvious way would be:


 * This introduces an extraneous equals sign into the derivation (before the arrow).


 * Can you point me to some proof that uses the eqn template in this way? Dan Nessett 14:33, 22 March 2012 (EDT)

Such constructions are all over the place. You should be able to find one quickly enough just by pressing "Random proof" a few times. You'll find it in the left hand column underneath "Navigation".

Quicker just to do it:

--prime mover 15:11, 22 March 2012 (EDT)


 * I was thinking the arrows should replace the equality signs and line up in the middle. But, it's your house and consequently your rules.


 * Given that, would someone take a look at the following and give some advice? There are two ways I can display the deduction in the proof (the previous suggestion leaves out the requisite conjunction). Here is one way:


 * Here is another way:

$ \displaystyle O\left[\nabla^m P_k\right] = k-m \ and \ O\left[w\left({x}\right)\right] = 2m \; $

I don't really like the look of either, since the first suggests there is some sort of connection between the first equality in the antecedent condition and the first derived equality. The second doesn't have this problem, but the derived equalities would really look better shifted to the right. Any suggestions on which option to use or perhaps another way to display the deduction so it looks a bit cleaner?

Dan Nessett 16:06, 22 March 2012 (EDT)


 * I'd simply go with:


 * possibly with a comment on the third line that it combines the above two, but I'm not sure how that could be concisely formulated. In any case, it is didactically quite important to stick with 'one equation per line' because not doing so would very likely lead to confusion. --Lord_Farin 16:49, 22 March 2012 (EDT)


 * Basically you got 5 columns for symbols and 2 for comments: ll, l, o, r, rr, c, cc. ll and l right-justify, o is center-justified, r and rr, and c and cc, are left-justified, so everything congregates into the center. If you omit the o command it defaults to the equals sign, so if you want the o column blank you have to specifically set it blank by donig "|o=" (the " are not part of the command of course).
 * You are completely free to align your equations with "o=\implies" (by the way, we always use \implies instead of \Longrightarrow for various no-brainer reasons, one of them being that it puts a small amount of extra space before and after) and put either side of the implications into l and r, and (if you're ingenious) working out how to make sense of putting equals signs in ll and rr. The reason the house style for these equations is as it is, is because of the design of the equation template, which has yet to fall short of presenting the appearance in a way that works for me, but that's just me.


 * Your original suggestion:


 * can be arranged thus as:


 * And, another incidentally, you should not need to do \; and so on except in exceptional circumstances - if you feel the need to add aesthetic spacing into the equation template, feel free to suggest an amendment to the latter. Having said that, in certain places it has proved desirable to put spacing in for readability, but these are few and far between. --prime mover 17:44, 22 March 2012 (EDT)


 * Thanks to both of you. Your comments are very helpful. Dan Nessett 18:08, 22 March 2012 (EDT)

Problem with alignment
I put a multi-equality equation into aligned format, but the result is less than satisfactory. Specifically, the equals sign in the aligned version isn't properly placed horizontally. Here is the original multi-equality version:

$ \displaystyle -\bar{f} \left({x}\right) \frac{d\left({p\left({x}\right) \frac{dg}{dx} \left({x}\right) }\right) }{dx} + g\left({x}\right) \frac{d\left({p\left({x}\right) \frac{d\bar{f} }{dx} \left({x}\right) }\right) }{dx} =\frac{d\left({p\left({x}\right) \left[{g\left({x}\right) \frac{d\bar{f} }{dx} \left({x}\right) - \bar{f} \left({x}\right) \frac{dg}{dx} \left({x}\right) }\right] }\right) }{dx} =\left({\mu -\bar{\lambda} }\right) \bar{f} \left({x}\right) g\left({x}\right) w\left({x}\right) $

Here is the aligned version:

Notice that the equals sign in the first line is above the fraction bar, which makes it appear misaligned. Perhaps this is an uncorrectable artifact of using MW tables. However, I thought I would ask in case there is a remedy. Dan Nessett 16:29, 23 March 2012 (EDT)


 * Looks perfect to me. Can't see a problem.


 * Oh beg your pardon, see what you mean.


 * It's an artifact of our equation template. Live with it is my suggestion. --prime mover 17:37, 23 March 2012 (EDT)

One sentence per line in theory articles?
House style stipulates that proofs place one thought/sentence on a line. Is this also true for theory articles? For example, I am working to bring an article on Sturm-Liouville theory into house style. There are several places where discussion is placed in paragraphs. Breaking each sentence out into a separate line would interrupt the thought flow. However, if that is what house style requires, I can do it. Dan Nessett 16:31, 27 March 2012 (EDT)


 * "Theory articles" as such have not been planned for on ProofWiki, as most of the contributors here are (or have been) contributing theorems in pure mathematics, where prolonged expositions of theory have not been necessary. In keeping with the spirit of ProofWiki, however, it is probable that it would be considered appropriate to split up a large article into several smaller parts, each one focusing on one small part of an extended dissertation.
 * As stated earlier, it is not the intention of this site merely to repeat existing encyclopedic pages as may exist on wikipedia or (as in this case) citizendium. ProofWiki is, to put it glibly, not an encyclopedia. It is more a dictionary. As such, a dictionary will be more likely to state, for example: "An aardvark is a southern African anteater (see South Africa, anteater)", while an encyclopedia will go into considerable detail as to everything there is to know about an aardvark.
 * I also point you towards the caveat at the bottom of this edit pane: "If you do not want your writing to be edited mercilessly and redistributed at will, then do not submit it here." It is an odds-on certainty that once posted up, it will be changed beyond recognition. This won't matter one bit, of course, because the article as you originally planned it remains on Citizendium, performing the task on that website for which it was designed.
 * But be that as it may, the prime rule is, as always, paste the damn thing up then we can muck about with it till we like it. Comes a time when, as the saying goes, you have to do something or get off the pot. --prime mover 16:58, 27 March 2012 (EDT)


 * I realize the content will be edited after it is pasted in the main namespace. My work at present is to be a good citizen and get the content as much into house style as possible before putting it there. However, if you don't want me to do that, that's fine. I will put what I have into the main namespace as it stands. Please make your desire clear.
 * With respect to the theory articles, I asked whether you wanted them or not here. Specifically, I asked:


 * "In regards to the theory pages. The only reason I mentioned them is that without the theoretical background, it isn't clear why anyone would be interested in proving the orthogonality properties. However, another viewpoint is anyone looking for such proofs would already be familiar with the underlying theory. So, the real question is whether ProofWiki has an objective for self-contained content."


 * In response, you wrote:


 * "Your last paragraph expresses a viewpoint which conflicts with the philosophy of ProofWiki. Every proof is dependent upon previously-established results and definitions, which in turn are dependent upon more fundamental results, and so on back until the axioms are reached (ultimately ZF(C) and whichever axiom schema of propositonal and predicate logic)."


 * So, I am a bit confused what is expected. I can put the orthogonality proofs here and leave the theory articles on CZ. But, I read your comments as suggesting that is not what you want. So, perhaps you would give me a direct answer. Do you want the theory articles? Dan Nessett 17:27, 27 March 2012 (EDT)


 * Well yes, certainly, ultimately we want it all. From my point of view: I'm waiting for them to go up as official pages, so that they can then be put into the appropriate format for ProofWiki, which will mean them being split up into sections, assigned to appropriate categories and links constructed as necessary to provide the context for each.
 * I'll let someone else answer the details of your questions as all I want is to get these damn things pasted up. I am a man of infinitesimal patience and would far rather get on with doing it rather than (as happens for far too much of my damn day in the thrice-damned office) sitting around in bloody meetings all day with people of the opposite persuasion, i.e. those who would rather talk than do. :-) --prime mover 17:47, 27 March 2012 (EDT)

So far so good ...
I hope you're okay with the direction the articles are going so far. My input has been to tidy up the $\LaTeX$ and make sure the presentation of the mathematics is in a consistent look-and-feel. I am also planning on extracting various self-contained sections and placing them into their own pages as and when such a modular approach makes immediate sense.

I see that the "S-L Theory" page as containing a series of transclusions, as suggested by the S-L Equation page, which can then be linked to and/or transcluded as required whenever this is relevant in the pages invoking it. As far as look-and-feel is concerned, that Definition:Sturm-Liouville Equation page is the style to aim for.

Superb start, by the way - this area is exciting and needs more attention than we have been able to give it so far (I'm more of a set theory and topology freak myself, and mediocre at that), so, as I say, all input is welcomed. The style is as always secondary to the content. --prime mover 16:02, 29 March 2012 (EDT)


 * No problems with the edits so far, except when you moved material into the Definitions namespace, some of the equation numbering broke. I have raised the general issue on the Main talk page. Dan Nessett 16:52, 29 March 2012 (EDT)