User talk:R.e.b./Archive 1

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Bernstein-Sato polynomial

Hello. Your editing on that article prompts some tips:

• The dot at the beginning of this sentence is a "bullet"; after a bullet any "displayed" TeX should get doubly indented, thus:

$\int _{-\infty }^{\infty }1\,dx$

whereas a single indentation suffices in non-bulleted material. Notice that the preceeding word "whereas" is indented (by the use of an initial colon that's invisible until you click on "Edit this page") because this paragraph is part of the bulleted item; otherwise it would have looked

like this.

• The title word or title phrase in any article should be highlighted at its first appearance, like this.

• When TeX is used on Wikipedia, it looks good when "displayed", but when embedded in lines of text it often looks too big or gets mis-aligned. Thus cos²(x) + sin²(x) versus $\cos ^{2}(x)+\sin ^{2}(x)\,$. (I think this may be browser-dependent so I don't know if you'll see the same thing I do.) Notice that I've italicized the variable x to match TeX style, but I have not italicized digits or punctuation marks or "sin" and "cos" (similarly "exp", "max", "log", "det", "sup", etc.). I've also put spaces before and after "+" (of course in TeX that gets done automatically).

Michael Hardy 23:13, 22 Mar 2005 (UTC)

Welcome to Wikipedia. You're making some intriguing edits. Charles Matthews 09:00, 24 Mar 2005 (UTC)

Links to pages you create

Hello. I've added Bernstein-Sato polynomial to the list of mathematical topics and also to the list of polynomial topics. I also created a page with the plural title Bernstein-Sato polynomials that redirects to Bernstein-Sato polynomial; that way anyone later tempted to create a page with the plural title will be made aware of the existence of the one with the singular title, and any links to the plural in other articles will also go to the appropriate place. If there are alternative names for the topic and you consider this one the best, you can create redirect pages to this one. Also, if you know of other pages that mention Bernstein-Sato polynomials but don't link to it, or that don't mention Bernstein-Sato polynomials but ought to mention them and link to the article, you may consider creating those links. Notice that in addition to the list of mathematical topics there is also the list of lists of mathematical topics -- in some ways a very interesting page. If you create a new mathematics article and then look at the "list of lists", you may find other lists to which the new article should be added. All of this brings the new article to the attention of other interested persons, especially to those whose watchlists contain the pages with the new links.

Also, notice that on any page, if you click on "what links here" you will get precisely that information. Sometimes you may create a new page and find that there are already many links to it, that formerly were "red links". Michael Hardy 23:15, 26 Mar 2005 (UTC)

More welcome

Let me welcome you too!

You might consider putting Wikipedia:WikiProject Mathematics on your watchlist — that's where all the math-related discussions on Wikipedia take place — and putting your name on the list of participants. Oleg Alexandrov 05:25, 28 Mar 2005 (UTC)

More non-TeX-nicalities

Hello again. Notice that in non-TeX mathematical notation, you don't need to write

H x K

for a direct product of groups H and K, since you can write instead

H × K.

Also, to match TeX style, one italicizes variables but not digits or punctuation.

And notice the difference between the following notations:

a-b

a-b

a−b

a - b

a − b

I always use the last of these; the spacing makes it more legible. And contrast these:

3^-2

3⁻²

the point being that a stubby little hyphen in a superscript or a subscript can by much harder to see than a proper minus sign. Michael Hardy 23:23, 14 Apr 2005 (UTC)

PS: The difference between

a + b

and

a + b

is not visible to the reader, but the latter will never allow a line-break between "a" and "+" nor between "+" and b. Since browser window sizes and shapes vary, that can matter if the whole expression a + b finds itself near the end of a line. So when "displayed" mathematical notation keeps it near the left side of the page, I don't bother with the non-breakable space characters, but otherwise I often use them. Michael Hardy 23:32, 14 Apr 2005 (UTC)

List of mathematical examples

I've added list of finite simple groups to the list of mathematical examples. You'll notice that the latter is a bit oddly organized, having a section for sporadic groups and another section for everything else. Maybe it will evolve from there eventually. But I wonder if the list of finite simple groups should appear in both sections? Michael Hardy 23:04, 17 Apr 2005 (UTC)

...and now it is in both sections. Michael Hardy 23:12, 17 Apr 2005 (UTC)

Conventions

I've added the Clifford algebra one to Wikipedia:WikiProject Mathematics/Conventions, which has only been around for a couple of days. The idea is that anyone with another view could go to the talk page there. Charles Matthews 17:16, 25 Apr 2005 (UTC)

outer automorphisms of symmetric groups?

Hello. I see you've been around here again recently. Since you know group theory, I wonder if some day you could write a Wikipedia article explaining the fact I've heard asserted, that the symmetric group on six elements is the only finite symmetric group that has any outer automorphisms (and maybe add it to the list of mathematical examples)? Michael Hardy 3 July 2005 02:44 (UTC)

I've added something like this to the page on outer automorphisms. If you're feeling idle it could do with some extra links. R.e.b. 3 July 2005 05:12 (UTC)

Table of Lie groups

Hi, I restructured the tables at Table of Lie groups, but as a result have gone cross-eyed. Could I ask you to proof-read this (and add any missing tidbits)? linas 20:39, 10 September 2005 (UTC)

I had a quick look, and didnt notice anything worse than a few minor missing bits and pieces. R.e.b. 21:35, 10 September 2005 (UTC)

Thanks, and question

Thanks for the above. Hate to bother someone twice in one day, but I have technical question. I'm wondering if you know of any lie algebras that look like this: they split into three spaces, one that is one-dimensional, call it j, and two others, call them x and y, such that

[j,x]=+x and [j,y] = -y

where by + and - I mean that the the structure constants are all positive, or all negative. The only example like this I know of is SL(2,R); I was wondering if there are any others; I'm hoping you might recognize this somehow. Thanks, linas 05:29, 11 September 2005 (UTC)

The heisenberg algebra and the virasoro algebra (without the center) and the elements of degree at least -1 of the latter algebra are three more examples. If you dont mind y being 0 you can take x to be any nilpotent algebra and j a suitable outer derivation. There are also a few Lie superalgebras with this property. R.e.b. 15:00, 11 September 2005 (UTC)

Thanks (slapping forehead)! linas 16:41, 11 September 2005 (UTC)

please vote

Wikipedia:Featured list candidates/List of lists of mathematical topics Michael Hardy 04:29, 13 October 2005 (UTC)

math vandal

User 161.184.8.128 has recently vandalized several math pages. I dont know how to sort this out, but I guess you do. R.e.b. 16:23, 11 October 2005 (UTC)

Looks like possibly a skeptical experimenter testing Wikipedia's integrity rather than a malicious vandal. I reverted all the edits and deleted the prank page on the non-existent mathematician, and no recurrences have happened for a couple of days, so maybe there will be no need to block that IP number. Michael Hardy 02:24, 14 October 2005 (UTC)

A TeX issue

Its elements can be written explicitly as pairs (A, f) where A = ${ab \choose cd}$ is in SL₂(R) and

If A was intended to be a matrix and TeX's matrix environment is too cumbersome when inline rather than dislayed, may I suggest this:

{a\quad b\choose c\quad d}.

What you get is this:

Its elements can be written explicitly as pairs (A, f) where A = ${a\quad b \choose c\quad d}$ is in SL₂(R) and

Michael Hardy 00:45, 24 October 2005 (UTC)

En dashes

We are now being told that we need en dashs to separate names in titles, so that it is the Birch–Swinnerton-Dyer conjecture for example and that can be parsed uniquely to two people. This is a bit of a nuisance really, but the en dash is at least available in the symbols below the edit box. The GHRR theorem is therefore giving ample scope for trouble. Charles Matthews 20:37, 9 November 2005 (UTC)

I've dealt with GHRR and redirects now, so Todd class does link. Charles Matthews 22:36, 9 November 2005 (UTC)

Boolean-valued model

Thanks for adding the section on Boolean-valued models of set theory. The construction part looks good. The last paragraph, on the metamathematics, has some problems, though. V and V^B are proper classes; we don't "prove they exist"; rather, we use them as predicates. I'll think about this a little bit before trying to fix it. --Trovatore 17:23, 13 November 2005 (UTC)

On reflection, I think maybe that para should just come out, and the metamathematical discussion deferred until a section on applications, like the currently-outlined "Relationship to forcing" section, or possibly a separate section on "Uses in independence proofs". After all, it's not relevant to the construction, which is what the section now seems to be about.

What is relevant to the construction, and is currently not treated, is how to code the individual elements of V^B by sets, rather than (as they would be if the construction were done carelessly) proper classes. --Trovatore 17:32, 13 November 2005 (UTC)

Sorry, this last doesn't look like a problem here. Not quite sure what I was thinking of at the moment. --Trovatore 17:41, 13 November 2005 (UTC)

"Allowing V to be set"

I don't agree with your word choice here. Of course we can create Boolean-valued models from set models, but then we would normally denote the set model as M rather than V (and we would have to note in the construction, at successor stages, that we're accepting only functions that live in M--and it gets even worse if we're not requiring M to be a transitive model; then we have to relativize the ordinals, too). There's really not much advantage to starting with a set model, though--if you're going to do that, then you might as well make M countable and transitive, and just force over it rather than using BVMs. The real conceptual advantage of BVMs is that you don't have to start with a countable transitive model, and you don't have to tell these awkward stories about generic objects that "don't really exist" (as you do when you force over V). --Trovatore 19:24, 13 November 2005 (UTC)

I've added some language to reflect the case where you start with a model M. --Trovatore 19:38, 13 November 2005 (UTC)

truth values

We ought to standardize the notation for the truth value (or "probability") of a formula, which right now is inconsistent between two sections. Looking at my refs, Bell uses Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): {\displaystyle \llbracket\phi\rrbracket} , which I guess is not available in Wikipedia (unless there's a Unicode for it somewhere). Jech uses ||φ||, like you. I think Bell's notation is a little nicer, but mainly we should be consistent, so if you wanted to change the notation in the earlier section that would be fine with me. --Trovatore 20:12, 13 November 2005 (UTC)

There is a Unicode. It would look like 〚φ〛. How well does that show up for you? I have to admit it's not exactly what I had in mind anyway. --Trovatore 20:44, 13 November 2005 (UTC)

The unicode 〚φ〛 works fine on my browser, but llbracket just produces an error message. The trouble with obscure unicode is that it may not work on all browsers, and the problem with two ['s is that it is a pain explaining to wikipedia that it is not a hyperlink. I vote for || || on the grounds that it is easy to type and does not cause problems. R.e.b. 20:54, 13 November 2005 (UTC)

I think you're right; sounds good to me. --Trovatore 22:28, 13 November 2005 (UTC)

Mathematical HTML

I moved this page to Wikipedia:Mathematical symbols and removed the libk to it from HTML as this article does not belong in article space. Cheers, —R. Koot 18:48, 25 November 2005 (UTC)

Mathematical HTML

I moved this page to Wikipedia:Mathematical symbols and removed the link to it from HTML as this article does not belong in article space. Cheers, —R. Koot 18:49, 25 November 2005 (UTC)

zero what?

Hi R.e.b., in List of large cardinal properties you added something called 0⁺. Is this supposed to be zero-dagger? I don't think the superscript plus sign really gets that across. --Trovatore 23:00, 29 November 2005 (UTC)

Yes, but the dagger symbol does not work on my browser, and this is the best I could do. R.e.b. 23:04, 29 November 2005 (UTC)