User talk:Messagetolove

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WikiProject Mathematics Talk

Thank you so much for your supportive comments and contributions. I'm very glad to see you have also added your name at Wikipedia:WikiProject Mathematics/Participants. I'm sure you also know that Wikipedia talk:WikiProject Mathematics is a lively forum where general issues that are not specific to a particular article can be be discussed.

On a personal note, thank you for your input and kind remarks on my efforts to include a few more articles under the umbrella of the project. I also feel obliged to echo the words of Oleg Alexandrov who welcomed me: "Don't forget: the edit summary is your friend!" Enjoy Wikipedia. It is generally a wonderful place, especially around the maths project. Geometry guy 19:43, 18 May 2007 (UTC)

Thanks for the welcome GG. Yes, WP (esp. Math.), seems like fun (perhaps too much fun, actually). I hope to write some original articles some day, instead of modifying existing ones- the 'Clifford's Theorem' section I put into the 'Character Theory page' could almost have been a separate article, but it does properly belong where it is, I think. BTW, I do occasionally lighten up!

Messagetolove 19:55, 18 May 2007 (UTC)

Erm, yes, a bit too much fun! I think we have a very similar WP philosophy. Anyway, before lightening up too much, I thought I should draw your attention to the latest information on the Newton-Leibniz controversy [[1]]. I certainly never expected such a surprisingly natural explanation for the centuries of controversy between two such brilliant minds. Meanwhile be bold starting new articles. Geometry guy 20:12, 18 May 2007 (UTC)

Yeah, I'd picked up on the Newton-Leibniz controversy link- quite subtle( didn't Cauchy beat them both to it anyway, or have I got the sequence wrong?).

Messagetolove 20:37, 18 May 2007 (UTC)

I think Newton and Leibniz came arbitrarily close, but Cauchy placed a limit on the validity of their methods. Geometry guy 12:27, 19 May 2007 (UTC)

This exchange is the sort of humor I like- compact, complete, yet totally unbounded.

Messagetolove 13:12, 19 May 2007 (UTC)

Mathematics CotW

Hey Message, I am writing you to let you know that the Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project. Any help would be greatly appreciated, thanks--Cronholm144 00:30, 14 May 2007 (UTC)

Thanks so much for your participation, I will keep you posted on our progress--Cronholm144 07:30, 14 May 2007 (UTC)

Complete metric space

Hi Messagetolove. Thank you for your edits at Complete metric space. I reverted them however, since you are making things rather complicated by making sure you first construct the real numbers as a complete space. That is not necessary, you can always assume that the real numbers are already defined and a complete space, otherwise you can apply exactly the same construction to the reals as for the metric space.

As such, there is no need to repeat the same construction twice.

Also, I have a few questions about style. One is that formulas should be indented only by one colon (:), and text should not be indented. Besides, it is good not to break lines in the middle of a paragraph, that is, not to insert newlines. The browser will wrap the text for you, and it looks better this way for people having a different width of the textarea box.

Thanks. You can reply here. Oleg Alexandrov (talk) 15:52, 4 June 2007 (UTC)

No, Oleg, I am afraid you are wrong, you have missed a subtle point. The way it is explained on the page, it says that the distance from one equivalence class to another is defined BECAUSE THE REAL NUMBERS ARE COMPLETE. But how can you use the completenesss of the real numbers to prove that the completion of the rationals is the real numbers? I certainly agree that once the real numbers are known to be complete, then one can use the more straightforward procedure to perform the completion of any other metric space. But you can NOT use the completeness of the real numbers in CONSTRUCTING the real numbers. This is why I made the remark about "avoiding circularity". The right way is to define the equivalence relation using the zero distance relation to put sequences in the equivalence class (and then, in the case of completing the rationals, strictly speaking, one should prove that the set of equivalence classes form a complete totally ordered field, which identifies with the real numbers). This is done with some care in Spivak's book for example. This is not a matter of style or taste, it is a matter of mathematical correctness and accuracy. What is in the reverted article is faulty. Messagetolove 16:57, 4 June 2007 (UTC)

I don't think the article aspires to prove that the real numbers are the completion of the rationals. As Oleg explained in the edit summary, this article assumes at the outset that the real numbers have already been defined and proven to be the completion of rationals, and continues to use this to show that any other metric space can also be completed. It is agreed that a separate proof for reals is required somewhere, just not in this article. -- Meni Rosenfeld (talk) 19:04, 4 June 2007 (UTC)

If that is the case, then it should be properly explained that the completeness of the real numbers is assumed from the outset, and the text "Cantor's construction of the real numbers is a special case of this; the real numbers are the completion of the rational numbers using the ordinary absolute value to measure distances." should be removed from the article, since this clearly implies that the construction described for a general metric space,which, as described, makes use of the completeness of the reals, is the same construction as used to complete the rationals (or anything else not already complete) to the reals, which could not make a priori use of the completeness of the reals. Furthermore, the explanation in the Edit Summary makes the incorrect comment that if we do not already assume the completeness of the reals, we could complete them by the procedure outlined for a general metric space. This is circular reasoning for the reasons I have explained already, as the completion process in the article uses the completeness of the reals. I really do not care greatly about my own text being reverted- I think my record shows that when my text has been reverted in the past ( a rare occurence to date) I have explained why the text was as it was, and not blindly reverted it back. But I do care that the text remaining on the page is incorrect.

Messagetolove 19:39, 4 June 2007 (UTC)

Post script: sorry, it wasn't in the edit summary that Oleg said that about completing the reals if they weren't already complete, it was on my talk page.

Messagetolove 19:56, 4 June 2007 (UTC)

PPS- In fact, the article does claim that any metric space can be

completed by the procedure it outlines, so this would/should include completing the rationals to the reals. Messagetolove 23:19, 4 June 2007 (UTC)

You are right of course, the completion of reals should be dealt with differently (I did not read your changes carefully enough). But I agree with Meni that Complete metric space is not the place for that. So hopefully we agree.

I have another small reminder about not using linebreaks in articles. For example, if you look at this diff, at the paragraph starting with "Georg Cantor..." you will see how newlines misformat the text.

Thank you for your math contributions. If you'd like to reply to me, you can reply here. Cheers, Oleg Alexandrov (talk) 02:26, 5 June 2007 (UTC)

r.

OK, I'll try to make things look better, but as I say below,

I don't want to spend a lot of time discussing style. I'm afraid that in the meantime, I had another attempt at describing Cantor's construction, but in a paragraph separate from the general case. Not as formal as before, and it explains the issue of why the completion of the rationals has to be treated slightly differently. If this is not the page to describe the reals as the completion of the rationals, then what is? Messagetolove 02:35, 5 June 2007 (UTC)

In the sentence

Assuming the existence and completeness of the real nunbers, any metric space M can be isometrically embedded in a complete metric space M' (which is also denoted as M with a bar over it), which contains M as a dense subspace.

I removed the part "Assuming the existence and completeness of the real nunbers,...". This is an assumption which is always satisfied, and all real analysis relies on it. This article is not the place in which to discuss the existence of real numbers. I think it is enough to mention, as you did below, that the actual construction of real numbers is not so simple as the completion of a metric space. No? You can reply here. Thanks. Oleg Alexandrov (talk) 02:40, 5 June 2007 (UTC)

to reply to your question above, about the right place at which to mention the construction of the reals, that place is Construction of real numbers. Oleg Alexandrov (talk) 02:41, 5 June 2007 (UTC)

Start again; I did not know about the "Construction of the reals page" this makes some difference to the discussion. You are right this time, about the fact that the embeddability of a metric space in a complete metric space does not depend logically on the completeness of the reals. However, the construction of the completion with the metric as described does depend logically on the assumption that the reals exist and are complete, so one has to spell out this assumption carefully if one is to make the claim that the construction works for all metric spaces. There are 2 choices: once could refer to the Construction of the reals page after pointing out the logical problem in assuming the completeness of the reals when trying to construct them. Or, one could give the careful construction of the reals as completion on this page, and refer on the general construction page to the Complete metric spaces page. Starting afresh, my preference might be the second. But it's late, and unlike you, I don't live in LA, so it's far past my bedtime . Messagetolove 03:26, 5 June 2007 (UTC)

Yes, the construction of the completeness of a metric space does depend on the assumption that the reals exist. The construction does refer to the fact that the reals are complete, see the section Complete metric space#Completion, under the formula

d(x,y) = lim_n d(x_n,y_n).

I agree that more careful wording could be necessary. Then, one could mention that one can construct the real numbers from scratch using a very similar approach, and refer to Construction of real numbers for details. What do you think? Oleg Alexandrov (talk) 03:40, 5 June 2007 (UTC)

Yes, that's the first option I outlined above, and seems OK to me.

Messagetolove 07:03, 5 June 2007 (UTC)

OK then. But I am not sure it is appropriate to actually start that section by saying "by assuming that the reals exist...". Perhaps only a parenthetical remark at some point during the actual construction, or something. I don't know. To me the article is already clear enough the way it is.

Let's do like this. If you modify that part of the article again I won't revert. But if I don't agree with your changes I'll comment here. Oleg Alexandrov (talk) 15:05, 5 June 2007 (UTC)

If you're happy with it as it is, that's OK with me. I kind of duplicate, in less detail, the construction of the reals by completion of the rationals which is given on the "Constructing the reals" page, which I was not aware of at the time, but that happens a ot in WP, and may not be so bad, as long as things are accurate.

Messagetolove 20:38, 5 June 2007 (UTC)

I feel that construction takes a bit too much space, but I guess it can't hurt (I may trim it at some point in the future, perhaps). Anyway, thank you for your patience in all this, and I am looking forward to more of your contributions in math articles. But note my earlier remarks about style, newlines, and indentation. Cheers, Oleg Alexandrov (talk) 01:47, 6 June 2007 (UTC)

Ratings and Style

If my style does not meet approved standards, then I apologise. I admit that I have been concerned more with content, though I am not inexperienced at Mathematical writing, and have tried to make things presentable, although I am as yet inexperienced in this particular medium. If anyone wishes to improve my layout, then please feel free to do so (I know that some already have, and that's fine). I don't want to spend time and energy debating style, though. Similarly, while I respect those who are dedicated enough to spend time and energy rating articles, I will not do so. I became interested in wp as a constructive exercise, and with an ideal of trying to improve and expand mathematical exposition. I have absolutely no desire to evaluate the efforts of others, only to clarify where I see possible ambiguity and inaccuracy, and explain where I perceive a gap that I have the knowledge to fill. I will comment on, or correct, inaccuracy, wherever I see it, and whoever is responsible for it. If that does not meet with the approval of those engaged in wikiproject Mathematics, then I can disappear as swiftly as I appeared. Messagetolove 21:41, 4 June 2007 (UTC)

Your contributions are most welcome in my opinion! Every editor should follow their own tastes in the edits they do: this is volunteer work, after all, and there is no point in working on something which doesn't interest you. And content, particularly technical content, is the most valuable work of all. Geometry guy 11:34, 5 June 2007 (UTC)

Have you taken a look at WP:MOS, and in particular WP:MSM? -- Meni Rosenfeld (talk) 15:10, 5 June 2007 (UTC)

Yeah, that's a good resource. Messagetolove, don't worry too much about style, you'll learn it as time goes on. :) Oleg Alexandrov (talk) 15:13, 5 June 2007 (UTC)

Oh, and another note, using a browser with a spell-checker, like recent version of Firefox, could be good too. (This is a small thing, but stating it once is better than fixing things many times afterwards. :) Oleg Alexandrov (talk) 01:32, 7 June 2007 (UTC)

OK, I agree that a spellchecker should catch typos. You should note, though, that "acknowledgement"

is correct UK spelling, and an acceptable variant, since you seem to be subjecting my edits to a high degree of scrutiny. Messagetolove 16:43, 7 June 2007 (UTC)

You are right about that, indeed. But not with the "additonal" though. :) And note by the way, that breaking lines, as you do above, misformats the text. OK, no more bugging, for now. :) Oleg Alexandrov (talk) 02:17, 8 June 2007 (UTC)

No, "additonal" was just a typo, and these do indeed happen, which is why I agreed above that spellcheckers are good for picking up typos.

Messagetolove 09:19, 8 June 2007 (UTC)

What (I think) Oleg tried to say about line breaks is -

If you are writing a comment, and making a line break, you need to put the colons again.

Otherwise, your sentences (or signature) will appear with different indentations, making the comment hard to read.

Also, there is no reason to put a line break in the middle of a sentence (there is automatic word wrap).

(Note: I've put many line breaks here intentionally, to demonstrate how to do them properly. In most circumstances you shouldn't use them this much).

-- Meni Rosenfeld (talk) 10:12, 8 June 2007 (UTC)

typo in "other theorems"?

(hi i thought i was gone from wikipedia, but i don't break away emotionally that easily.) In Fermat Numbers please doublecheck for typos in your edit to other theorems section. Regards, Rich Peterson

I took a look Rich, and didn't see a problem, though it's easy to be blind to typos in your own edits ( I see a confusing line break,which doesn't help, on my screen). You must have had something specific in mind(?) Messagetolove 08:06, 12 June 2007 (UTC)

PS: I noticed a missing "is" eventually. I have rearranged a lot now anyway. Messagetolove 20:58, 12 June 2007 (UTC)

Principal ideal domain

I like the way you introduced this article. I don't care for what is usually the "house style" around here, which is to specify a context with two or three words and force a terse definition into the remainder of the first sentence. A good example is the introduction you replaced.

The price of leaving out redundant information is paid by the reader who fills in the giant gaping holes by heavy use of the hyperlinks, which unfortunately lead to articles that are similarly introduced.

For what it's worth, I think I'll try to do it your way from now on.

Cheers, some other anonymous fool

Thanks, fellow anonymous fool!

Messagetolove 23:07, 22 August 2007 (UTC)

Group theory general plan

Hi Messagetolove, can you, please, help with designing a grand plan for Group theory? There is currently a discussion under way, and this may be a unique opportunity to steer the article in the appropriate direction. Also, if you find a way to incorporate your remarks about the general scheme of the classification of finite simple groups into the body of the article, that would be swell! Regards, Arcfrk (talk) 02:47, 11 July 2008 (UTC)

P.S. It looks like you are not editing very much lately, hopefully, you check this page occasionally.

Hi Arcfrk: I'll try to contribute. 20:46, 13 July 2008 (UTC)

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