User talk:Linus44

Welcome
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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)

Comments, then ...
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 . 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)

Internal links
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)