# User talk:Linus44

#### Welcome

Welcome to ProofWiki! Since you're new, you may want to check out the general help page. It's the best first stop to see how things are done (next to reading proofs, of course!). Please feel free to contribute to whichever area of mathematics interests you, either by adding new proofs, or fixing up existing ones. If you have any questions please feel free to contact me, or post your question on the questions page.

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Cheers, prime.mover (talk)

## Properties of Degree

We're obviously on precisely the same page here (literally!) as this was the next proof (after tidying up after the infrastructure update) that I was going to post! You're not working your way through Hartley and Hawkes yourself, are you?

Keep up the damn fine work, bro - and bear with me when I reformat stuff into our (so far unwritten) house style. --prime mover 00:48, 8 February 2011 (CST)

Just read your comment (later deleted) on polynomials: if you have a strategy for axiomatic foundation of Galois theory, then feel free to go for it. You've noticed there's a lot of groundwork done already - but the author of most of this (ahem, me) has little background in it except what's been self-taught, so feel free to rewrite or amend if stuff is insufficiently precise or accurate. And if you have an idea of how to turn into crystal the amorphous sludge that currently constitutes the section on polynomials, then go for it. --prime mover 00:59, 8 February 2011 (CST)

## The big picture

You're obviously focused here - I'll let you get on with it as you definitely seem to be in the zone.

You just happened to turn up as we're in the middle of changing the infrastructure to use a new LaTeX package MathJax. Some of the old commands no longer work like \or and \and - I'm replacing them with \lor and \land as I go - and display text formatting insists on centre justifying, which doesn't work too well here.

It'll shake itself down in time, no doubt, but in the meantime expect plenty of pages to not look as good as they should. IF you see any then feel free to try and fix them, and if you have problems let me know and I'll see what I can do. --prime mover 00:22, 9 February 2011 (CST)

... Just pick it up as you go along, you're all right.--prime mover 00:46, 9 February 2011 (CST)

You said "comments welcome, okay then ...

Nice job. In the groove.

There's a few stylistic and "house standard" issues which you may want to take on board (not to worry if not, it'll get changed).

• Good to separate each entity in LaTeX with a space - a rule of thumb is put a space between each variable and before each backslash starting a command. It's not important, but it makes it readable and allows for a saner line breaking.
• More tediously, anything parenthesised ought to be between $\left({ left and right }\right)$ delimiters. Not sure if this is relevant any more actually, but with MediaWiki in particular this enforced the browser to space things neatly, even in cases where what's in the middle is a single letter. E.g. $f \left({x}\right)$ not $f(x)$. This needs to be waived, of course, if the brackets involved are in different latex strings.
• You've noticed that the delimiter of choice is now dollar not < math >. The latter renders still, but interestingly not in transclusions (see Trigonometric Identities for an example of lots of transclusions). There is an ongoing exercise to convert all math delimiters to dollars.
• Finally (this time round), the writing style here is (barring the occasional page or two in symbolic logic written by someone who didn't get it) "short and sweet."
Long sentences are likely to be split up into shorter ones.
Each sentence needs to go on a separate line.
The result is that it is easy to follow.
The above fact continues to hold even when the proof is tortuously complex.
• Other minor stylistic quibbles are relatively inconsequential: display equations aren't punctuated with a full stop (that's an Ian Stewartism), lines before a display equation end with a colon:
because this is a display equation

and punctuation does not go inside a latex object (despite what they say on wikipedia).

That is:

Hence the result for $f(x)$.

not:

Hence the result for $f(x).$

And yes I know I've broken more than one of the above rules in the above.

Keep on trucking.--prime mover 13:34, 11 February 2011 (CST)

## Numbering equations and referring back

Like this:

$\label{einstein} e = m c^2$

Then you can refer back to \eqref{einstein} like this.

This is new with the MathJax package.

I'm not sure how limited we are on how such equations may be formatted. I'm not a fan of centre justification on a wiki page as it doesn't lend itself to the eye when the sentences are short. I haven't found a way to define the default for display equations to default to left justification. I believe you can do it in standard LaTeX documents (long time since I wrote one) so it ought to be doable here.

What I tend to do in the meantime is do it manually:

$(1) \quad e = m c^2$

Then you can refer back to $(1)$ like this.

--prime mover 02:13, 12 February 2011 (CST)

## Help page

Wow! Nice one. That was something I was going to get round to doing one time. Saves me a pain! Thx. --prime mover 02:18, 12 February 2011 (CST)

... in fact it encouraged me to work on it. --prime mover 04:11, 12 February 2011 (CST)

## Pointwise operations

We already have a page for this. I think it's in the Abstract Algebra category. Might take some hunting down - sorry, been called away for domestic reasons - I'll get back to you on it. --prime mover 06:21, 13 February 2011 (CST)

You wrote: "... the definition of induced structure is quite robust so it covers addition (although interestingly not [I think] multiplication) of polynomial forms as well ..." I don't see why not, if you treat the concept of $\oplus$ as being either multiplication or addition. Can we continue this discussion in the talk page of Definition:Induced Structure? I need to understand what you're thinking. --prime mover 08:35, 13 February 2011 (CST)

... Goodness. It'll take me a while to digest all that lot ... bear with me, I'm only able to bear a subset of my braincells at the moment. I never dreamed it would have been so involved. --prime mover 09:56, 13 February 2011 (CST)

## Defining operators

If you need to define an operator in $\LaTeX$, rather than use \text{op} for example, use \operatorname{op} instead. There's a reason for this: apparently it gets rendered differently so as to be more appropriate to being an operator (more space afterwards perhaps) in certain browsers. Or something. It's what we've been doing up till now. Probably no big deal, it's just a nicety.

We may find that \operatorname isn't what's supposed to be used now anyway, it's probably \mathop now - but I'm not in a position to experiment. --prime mover 00:45, 17 February 2011 (CST)

Sure thing, it appears that \mathop is for turning a composition of symbols into a single operator, e.g.
$\displaystyle \mathop{\bigoplus \bigotimes}_{1\leq i< j \leq n} (ij)$
while \operatorname is for operators with textual names, hence makes a better standard of \id etc. At least I think those their intended purposes. Linus44 13:39, 17 February 2011 (CST)
backslashed your LaTeX for yez --prime mover 14:53, 17 February 2011 (CST)

## Macros

Replied on my page: --prime mover 15:07, 20 February 2011 (CST)

I'm interested as to your techniques for including internal links in your articles because I see they have the underscores in them. Not a big problem (can make it more tedious to produce a form for reading because then it forces you to format it) - but I'm curous as to what your technique is that makes this easier than writing the link without the underscores. --prime mover 00:25, 23 February 2011 (CST)

## ... unrelatedly

While the Principle of Mathematical Induction implies Well-Ordering Principle, as proved on Equivalence of Well-Ordering Principle and Induction, it is not the case that the Well-Ordering Principle implies the Axiom of Choice.

The latter is implied by the Well-Ordering Theorem (not documented yet), which states that any set can have an ordering under which that set is a well-ordered set. But that latter is NOT the Well-Ordering Principle.

Good question. --prime mover 00:41, 23 February 2011 (CST)

Ah, my book has the WOP as "every set can be well ordered". I was wondering why no-one had told me about that incredible set of equivalences. Thanks! --Linus44 00:48, 23 February 2011 (CST)
There is a word in the WOP defn on this site warning not to confuse the WOP with the WOT - perhaps it needs a further word about how the WOT is also sometimes called the WOP! Scary biscuits ... --prime mover 01:57, 23 February 2011 (CST)

## Listen here wolfchild

... I speak to you of the science of mythology ... :-)

Good catch. --prime mover 14:43, 23 February 2011 (CST)

## big thankx

for helping with this tedious migration. Your effort is appreciated. --prime mover 15:14, 3 March 2011 (CST)

S'alright, I just figured out external editing in Chrome; the equations load about 10 times quicker than they did in Firefox so it's quite relaxing to do now --Linus44 23:50, 3 March 2011 (CST)

## Sorting definition pages

When you categorise a new definition page, plz remember to add |{{SUBPAGENAME}} to the definitions category - otherwise the category page will sort it on "Definition:..." and therefore put it under D where it ought to be sorted as the subpage name. (Note to self: check this is stated in the edit help pages.) --prime mover 17:35, 4 March 2011 (CST)

Ah yes sorry, I had picked up on that....then forgotten again --Linus44 01:46, 5 March 2011 (CST)
... no big deal, we can correct them as we find them.
Underneath the edit pane there's a "MediaWiki Functions" box which you can use to put the template for a category, definition category, etc. in place without having to type it in. Just click on the appropriate blue thing and a copy appears where your cursor is. Might be worth getting the habit then it's just muscle memory. --prime mover 03:23, 5 March 2011 (CST)

## Minor changes

Something to beware of (I'm always doing it myself!) is hitting the "minor edit" check box when you don't want to, and you especially don't want to do it with a new proof. In the latter case what happens is that the proof does not get logged as the "Latest proof" (on front page) or added to the list of "recently added proofs" (see Community portal), and you lose the kudos. --prime mover 17:02, 27 March 2011 (CDT)

Ah yes, had it marking as minor by default, now changed. --Linus44 17:08, 27 March 2011 (CDT)

## Properties of Gamma Function

Just a heads up: what I did with Properties of Gamma Function was split it up into 4 separate pages linked by transclusion. It's the same technique as I used on Properties of Binomial Coefficients, q.v. for comparison. The individual results all merit a page of their own (particularly the ones with names on them) and besides they'll probably end up being too big for comfort. Big pages don't work too well on this wiki. --prime mover 15:59, 29 March 2011 (CDT)

Works for me --Linus44 09:36, 30 March 2011 (CDT)

## Does not divide

Using nmid. See Definition:Divisor Notation where the notation is discussed. It's not a perfect solution but using slash to negate a backslash makes something ugly. --prime mover 01:34, 3 May 2011 (CDT)

## Using newcommand


If we can solve these problems (I confess they're not high on my list ATM), then I wonder whether it might be feasible to set up some "standard" abbrevs for some stuff, a) because it will streamline certain pages, and b) because it will then give us a basis for a "uniform" symbology.

One thing I've been meaning to get round to (but there's always exciting results to document instead) is a list of standard symbols (as part of "house style") like using $\varnothing$ for the empty set rather than $\emptyset$, and $\backslash$ for "divides" and not "\mid" and so on. Using a standard header file with "newcommand" commands in may give us a headstart on that experiment.--prime mover 16:10, 6 May 2011 (CDT)

Yeah, the newcommand stuff was just because I prefered $\operatorname{Max}\:\operatorname{Spec}$ to $\operatorname{MaxSpec}$, but the former takes forever to type.
Uniform notation would have it's advantages, but then it'd be good to have a more obvious link on each page saying "The notation used is explained here", otherwise there's a risk of being difficult to read for anyone unfamiliar with these pages, especially with stuff like $\backslash$, where $\mid$ is more commonly used. --Linus44 07:22, 7 May 2011 (CDT)
My approach to this is always, when using a piece of notation which is possibly non-standard or unusual, to add "... where $\backslash$ denotes divides" or whatever. How do I know whether it's non-standard enough to merit this? Someone complains they can't understand it. :-) --prime mover 08:14, 7 May 2011 (CDT)

## Welcome back

I thought you'd gone forever! --prime mover (talk) 05:51, 28 September 2012 (UTC)

I've been making do with the internet on my phone for ages, since I never used it for much more than emails. I'm not sure how often I'll be on here, the spare time I do have is usually a much needed break from mathematics, but we'll see. --Linus44 (talk) 16:41, 28 September 2012 (UTC)

The recent edit you made to Definition:Differential has completely obscured the basic simplicity that it originally was and cast it into language which is inaccessible to undergraduates. We're trying not to lose the basic understandability here, and besides, the citation at the bottom of the page no longer has anything to do with what's on the page.

You might want to take some time to refamiliarise yourself with the house style and the general philosophy of this site - the idea is for it to be more of a dictionary than an encyclopedia. In particular, I believe that what we might want to do with this page is to write the more complicated stuff in a separate page and transclude it. --prime mover (talk) 19:26, 28 September 2012 (UTC)

This is a point. It might be good to split the definition up into sections of successive generality, with the $\R \to \R$ setting at the top. I'll rearrange it after I've eaten some chocolate bread.
BTW, is there a page for vector spaces of the same dimension are isomorphic? There seemed to be enough linear algebra that it ought to be there, but I couldn't find it. --Linus44 (talk) 20:26, 28 September 2012 (UTC)

## SourceReview template

Please add an invocation of Template:SourceReview at the bottom of any pages which you have refactored, like for the Gauss's Lemma page. It allows someone coming after to note the fact that the process flow of the works that are invoked can be amended as appropriate. --prime mover (talk) 06:23, 19 March 2013 (UTC)

ok --Linus44 (talk) 11:11, 19 March 2013 (UTC)

## Fundamental Theorem of Algebra

Thanks for polishing up my proof! :-) It was my first attempt to write a proof here, so I'm really grateful for your corrections and additions. --BFeuerbacher (talk) 20:36, 16 April 2013 (UTC)

No worries, and thanks for your contribution. My changes were just cosmetic stuff and adding links to the results used, see here for an explanation of the changes. --Linus44 (talk) 22:23, 16 April 2013 (UTC)

## Question about Definition:Partition of Unity (Topology)

I have addressed some of the unclarities in this page, but there is still an outstanding question about what is specifically meant by "support" - there are two definitions on that page which appear to be mutually incompatible.

Are you in a position to be able to go back to this page and see whether (a) it is still accurate, and (b) it needs improvement? I gather you may be more familiar with this area of maths than I am - and besides, you wrote the original (presumably in support of the Stokes' Theorem page) ... --prime mover (talk) 07:52, 15 September 2013 (UTC)