User talk:EmilJ/Archive 3

Archive 1

Archive 2

Archive 3

Archive 4

zeta equivalence with product of reciprocals of differences of 1 and -s power of all primes

We recently disagreed on a topic concerning a rather elementary result concerning this sequence. I found a page that would help you out http://mathworld.wolfram.com/RiemannZetaFunction.html scroll down by searching for the string 'An unexpected and important formula' and read it there. It's also explained on the page we had our disagreement on. You'll notice a general sieving process employed by Euler and then you'll how Euler's statement that (zeta(1) = divergence) -> (infinitude of primes) is a flawed implication. --DWB —Preceding unsigned comment added by 76.182.194.195 (talk) 02:44, 16 April 2010 (UTC)

Czech Republic – Iceland relations

The article on Czech Republic – Iceland relations is up for deletion, do you have time to see if you can add any new references? --Richard Arthur Norton (1958- ) (talk) 20:50, 10 June 2009 (UTC)

Abuse Filter Log

Can I bring this to your attention please [1]. Apparently you have violated two accounts of "Macedonia name conflict". However you have not actually done anything wrong. I am in the same position as you, see here [2]. We have both done nothing wrong, but this "Macedonia name conflict" has been added to our "Abuse Filter Log". I think this is really unfair. I have complained here [3], please feel free to participate because we have both been accused of something which we didn't do and we haven't even been consulted about this. This is really unfair. Regards Ijanderson (talk) 18:41, 25 June 2009 (UTC)

My understanding is that this is not something to worry about. The filter is triggered by pretty much any changes of Macedonia, Republic of Macedonia, or FYROM to each other, it is expected to generate false positives, and that's precisely the reason why the only enabled action of the filter is to log the hits, rather than disallowing the edit or warning the user or some such. — Emil J. 10:32, 26 June 2009 (UTC)

Thanks, I just wanted to make sure you knew. Apparently there is something wrong with the filter. Regards Ijanderson (talk) 10:53, 26 June 2009 (UTC)

Albanian embassy in Kosovo

You're quite right - I was getting Afghanistan and Albania mixed up... Bazonka (talk) 17:09, 16 July 2009 (UTC)

On behalf of retrieving archived discussion on Talk:International recognition of Kosovo

Perhaps my action of retrieving the archived discussionmay be interpreted as conforming to WP:IAR, but your action of archiving the ongoing discussion is interpreted as conforming to WP:IAR, without regard of WP:Consensus. I took the liberty and "disarchived" the discussion because I consider the discussion ongoing and not over. Especially since the words "...and there's no benefit in keeping it here" by the editor who asked for its closure haven't given enough justification for his/hers request. There's no benefit cannot by any mean be verifiable, not to say true, simply because my own opinion does have to matter, and giving my opinion on this subject should be considered as benefit. Of course when you assume WP:AGF|good faith) on my behalf, as I hope and honestly believe you do. All the best, --Biblbroks's talk 12:01, 21 July 2009 (UTC)

There's been no sign of any ongoing discussion for over two weeks, apart from one isolated post. Despite your self-chosen username, you are not the president of the universe, so there is no reason why we should keep your opinion on the talk page indefinitely. You stated your opinion, other people stated theirs, the discussion is over, it gets archived. Stop your disruptive editing behaviour, WP:IAR is for rare exceptional situations, you cannot appeal to it all the time just because all other editors of the page disagree with you. — Emil J. 12:13, 21 July 2009 (UTC)

Barnstar

		The Barnstar of Good Humor
		I don't give Barnstars very often, but your comment regarding the misspelling of Zaphod Beeblebrox made me laugh. Therefore you deserve the Barnstar of Good Humour. Regards Ijanderson (talk) 19:26, 29 July 2009 (UTC)

Wow, thanks! — Emil J. 09:54, 6 August 2009 (UTC)

scaling a formula

Dear friend, Thanks for your help at help talk:Displaying a formula. I posted a new question relating to "scaling a formula". Could you please help? Thanks in advance! Best regards
‫·‏לערי ריינהארט‏·‏T‏·‏m‏:‏Th‏·‏T‏·‏email me‏·‏‬ 11:51, 11 August 2009 (UTC)

Wikipedia:WikiProject Logic/Standards for notation

Hi, you reverted my edit to Wikipedia:WikiProject Logic/Standards for notation. I reverted it back, because in <math>, \& produces error ($\&$), but \And produces the right output ($\And$). Svick (talk) 09:56, 2 September 2009 (UTC)

Sorry, you are right. It did not occur to me that texvc could have such a weird incompatibility with standard TeX. — Emil J. 10:04, 2 September 2009 (UTC)

Balkans

VERY SORRY --Factuarius (talk) 16:32, 2 September 2009 (UTC)

No problem. I hope that our little misunderstanding is now resolved. — Emil J. 16:52, 2 September 2009 (UTC)

Minor edits

Please don't mark non-minor edits as minor, like this one. See Help:Minor edit:

"When not to mark an edit as minor:

• Adding content to an article
• Removing content from an article"

Thanks for adding the information on JSL to the linked article, to avoid surprising the readers who click through the dab page. -- JHunterJ (talk) 11:07, 3 September 2009 (UTC)

Linearly independent characteristic functions

Hi Emil. After your quick counter-example to my naive hint here I happened to think a bit on it. Here is an obvious but nice construction of a monotone (wrto inclusion) family of subsets of $\textstyle \mathbb {N}$ $\textstyle \{S_{x}\}_{x\in [0,1]},$ such that $S_{x}$ has density $x$.

Consider an equidistributed sequence $\{\alpha _{n}\}_{n\in \mathbb {N} }$ in $[0,1],$ and define

$S_{x}:=\{n\in \mathbb {N} \,:\,\alpha _{n}<x\}.$

Then, by definition, $S_{x}\subset S_{y}$ for all $x<y$ and $d(S_{x})=x$ for all $x$. As a consequence, in any finite collection of $S_{x}$, one of them is not covered by the others (so their characteristic functions are linearly independent &c). --pma (talk) 07:51, 28 September 2009 (UTC)

Yes, this sounds right. — Emil J. 11:24, 28 September 2009 (UTC)

TeX

Capitalization rules of Wikipedia are followed by other pages, such as flOw. Just because a name isn't capitalized and is widely spelled a certain way doesn't exempt it from the standardization. Talk to me, Rbpolsen♦☺♦ 04:32, 30 September 2009 (UTC)

You misunderstand Wikipedia naming conventions. The most fundamental rule is that articles are normally titled using the most common English-language name of a person or thing that is the subject of the article. So, yes, the fact that the name is widely spelled a certain way does in fact make it the title of choice. The MOS:TM guideline you quoted merely elaborates on this convention by stressing that if there is a discrepancy between common English usage and a trademark, the common English name prevails. This rule is actually redundant (it already follows from the first rule), and in any case, it is not applicable to TeX, because here the common English usage agrees with the trademark. — Emil J. 11:47, 30 September 2009 (UTC)

Excuse me

You said, Fix your computer instead of breaking it for all other people. In what way does my computer need to be fixed? I've never seen this problem on any other article, and I've edited several thousand. Jehochman ^Talk 13:09, 2 October 2009 (UTC)

First of all, what problem are you talking about? I can't even try to tell you what needs to be fixed before you tell us how is it broken for you. However, since the pronunciation info is a simple string of Unicode characters, most likely it is due to missing or incorrect fonts. — Emil J. 13:18, 2 October 2009 (UTC)

That I can see because many of the characters appear as little squares. My system has all the default US-English Windows fonts. I did not remove any. This is a problem I have not noticed on any other article ever. For instance, the template works fine for me on Johann Gottlieb Fichte. Jehochman ^Talk 13:21, 2 October 2009 (UTC)

The sets of characters used in transcriptions of the two names happen to be almost disjoint, so this does not say much. Did you check what characters you do or don't see at WP:IPA for German? Anyway, I can't help you much with Windows fonts, you should direct your question to WP:VPT or WP:RD/C. — Emil J. 13:41, 2 October 2009 (UTC)

Your indent question

About your question: "is there any particular reason why [I] keep making [my] posts one-element unnumbered lists?" Well, I'd noticed that the sys-ops were starting their posts like this on a certain page. I can't seem to find the page right now. I think it makes it easier to see where my posts begin. If we all adopted it then it would work much better. At the moment we have some messages following each other with the same number of indents and the signature is the only clue as to where one post ends and another starts. I hope it's not too offensive to your eyes. ~~ Dr Dec (Talk) ~~ 17:25, 8 October 2009 (UTC)

If we all adopted it: maybe, maybe. The catch is, we didn't. The standard on WP talk pages is to use colons rather than bullets, and then if there is a lone post starting with a bullet in the middle of a thread, it has rather the opposite effect from what you intend: it makes it harder to figure out where the post fits in, as it is misaligned with the rest, as well as simply looking unusual. Bulleted (or sometimes even numbered) lists are generally used only in polls (like WP:AfD) and similar situations, where it helps to quickly numerically gauge the current consensus. — Emil J. 18:14, 8 October 2009 (UTC)

Well, if you feel so strongly about it then I'll have to reconsider. ~~ Dr Dec (Talk) ~~ 18:16, 8 October 2009 (UTC)

By all means use whatever formatting you want, I was just wondering. — Emil J. 18:23, 8 October 2009 (UTC)

IPA keyboard input

EmilJ, I appreciate the fact that Wikipedia articles should not normally refer to themselves. However, I think an exception can be made for a brief mention in an appendix to an article. This is not harmful and could be helpful. I refer you to Wikipedia:Help desk#More on IPA tone for an example of the kind of frustration that can be caused by having no reference whatsoever. Please reconsider these deletions in the International Phonetic Alphabet article. --seberle (talk) 15:26, 13 October 2009 (UTC)

There is no reason why any editing tools should be mentioned in an encyclopedia article on IPA. It is harmful, just like adding any other non-encyclopedic material. Such things belong elsewhere, such as WP:IPA or (some of the subpages of) WP:EDIT. — Emil J. 15:49, 13 October 2009 (UTC)

Ok. I have added a link to the appropriate manual. Such things may belong elsewhere, but there needs to be a way to get elsewhere, and currently the path there is not clear. I know. I spent hours looking for this resource. --seberle (talk) 15:53, 13 October 2009 (UTC)

Seberle, there is no point having a self-reference within the article; the article is written for people who read Wikipedia, not people who write it. Any information on keyboard input should be in the dablink at the top of the article, if anywhere.

The Helpdesk link you've given contains nothing (as far as I can tell) showing a consensus to include this self-reference. Therefore, I am removing it. rʨanaɢ ^talk/_contribs 16:45, 13 October 2009 (UTC)

I see your points, but something still needs to be done. Perhaps you have a suggestion? There are two problems with the link at the top of the article, and someone needs to address them. First of all, the link to Help:IPA just says it is for "pronunciation guides", so anyone trying to figure out how to type IPA code would not follow that link. Secondly, even if you do follow that link, there is really no information in there on how to enter IPA codes. My recommendation would be that the Help:IPA article be updated (as others suggested at Wikipedia:Help desk#More on IPA tone) and then that the link say something like "pronunciation guides and editing tips" or whatever. But perhaps you have a better idea? I am definitely open! This really should not be as difficult as it now is. I'm not sure what you mean by "nothing showing a consensus". The link is, in fact, a collection of rather generic means of entering IPA code, most of which are applicable not only to Wikipedia, but anywhere. It is more helpful than the other Keyboard Input links in the IPA article. Oh, well. If including a small link is not acceptable, please come up with other suggestions on how to help people figure out how to enter IPA code. Thanks for any ideas you can come up with. --seberle (talk) 17:26, 13 October 2009 (UTC)

The external links section already has a bunch of links to keyboard input methods. It's not our job to point out which specific methods are good for Wikipedia use (as opposed to other use). There are already more than enough input methods and copy-paste methods in that section for any user to get by. rʨanaɢ ^talk/_contribs 17:58, 13 October 2009 (UTC)

Do you mean the External Links in Help:IPA? There were only two links, neither of which gave any help for inputting IPA to a Wikipedia article. I just added the third link, which does help. This is supposed to be a help article for Wikipedia editors, so of course it is "our job to point out which specific methods are good for Wikipedia use". If you mean the External Links of the International Phonetic Alphabet article, there are 12 and only one is helpful for Wikipedia editing (unless you have a Mac). In this case, having "more than enough" is actually less helpful. I was simply trying to leave a hint to future editors which link was the one they needed. But I accept that this is against Wikipedia policy. That's cool. But what we need now is more explicit help in the Help:IPA article, and I do not have the expertise to do this. I might resort to simply copying the helpful section in Wikipedia:Manual of Style (pronunciation)#Entering IPA characters. I can at least do that. --seberle (talk) 23:04, 13 October 2009 (UTC)

Be bold

but then discuss; see WP:BRD. Your changes to sinc function and what you're saying about them don't make sense to me, but maybe if you explain better I'll get it, or some other editor will support it and explain why. But I doubt it. Dicklyon (talk) 15:50, 16 October 2009 (UTC)

Sieve of Atkin

I found your comment on Sieve of Atkin to be maybe wrong [4] as the paper cited (http://cr.yp.to/papers/primesieves.pdf) specifically states that "One can save a factor of log(log(N)) in the running time of the sieve of Eratosthenes by letting W grow with N". I was unable to reach the O(N^1/2(log log N)/log N) bound on memory so I left that untouched. No hard feelings, and if I'm wrong, leave me a message on the Sieve of Atkin's talkpage because I can't be reached through this dynamic IP. =) —Preceding unsigned comment added by 75.4.226.28 (talk) 04:44, 21 October 2009 (UTC)

The basic form of the sieve of Eratosthenes takes time O(N log log N). Letting W grow with N indeed saves a factor of log log N, resulting in O(N) time. — Emil J. 09:55, 21 October 2009 (UTC)

Thanks, you're correct. 75.4.226.28 (talk) 01:04, 22 October 2009 (UTC)

Bertrand's postulate

Hello, could you explain the mathematics behind this edit? I'm probably missing something simple, but I don't see how it follows. Thanks, Shreevatsa (talk) 23:55, 26 October 2009 (UTC)

Oh sorry, nevermind, it was pretty simple indeed. I'll add some explanation to the article just in case. Shreevatsa (talk) 01:28, 27 October 2009 (UTC)

MA contained in AM

Hey, I noticed you removed a line from the article on Arthur–Merlin protocol, which explained why MA is contained in AM. You mentioned that "This explanation is nonsensical, the actual argument is somewhat more difficult." I didn't add the original text myself, but I don't see the problem with that explanation. What am I missing? --Robin (talk) 23:42, 16 November 2009 (UTC)

The "explanation" was that Arthur need only send a void "query" at the start, to which Merlin will respond with the information it needs to send under the MA protocol. If Arthur sends a void query, there will be no randomness in the protocol, in other words, the text was actually claiming that MA = NP (but did not give any argument how Arthur is supposed to verify Merlin's answer after he forfeited his access to random bits). — Emil J. 10:59, 17 November 2009 (UTC)

Ok, I see the confusion is because I thought Arthur always has access to randomness in the last stage when he outputs 0 or 1. So in an AM protocol, Arthur can only send random bits to Merlin, and his last step has to be a deterministic computation based on all messages received from Merlin and the random bits he has sent in previous rounds. That clarifies things. Thanks. --Robin (talk) 14:10, 17 November 2009 (UTC)

Big-O Notation Discussion Page Deletions

RE: "Such edits are disruptive and appear to be vandalism."

The deletions were intentional and very appropriate.

I don't believe Wikipedia's discussion pages are intentionally designed to be used to store concluded discussions forever. It is inconvenient ("disruptive") to users and gets in the way of improvements to Wikipedia itself.

The discussion page is long enough to make it intractable, I simply removed those discussions that had come to a decision and other discussions that had no relevance (like the 'should I write some other article' one).

It is unfortunate if you have reversed all the deletions I made. I thought I was very strict in my selection and would hope that you would have personally verified that the edits were inappropriate for each case before reverting the clean-up.

121.210.170.141 (talk) 11:43, 18 November 2009 (UTC)

If you think the talk page is too long, suggest on the talk page to set up an WP:archive. Plain deletion of other people's comments is absolutely unacceptable behaviour. See WP:TPG. — Emil J. 11:50, 18 November 2009 (UTC)

You're probably right for the most part. I was just trying to save other people's time, and wrongly expected that once reviewed, the changes would be accepted.

It is not "absolutely unacceptable" behavior to delete comments, as I quote from the TPG:

"Editing -- or even removing -- others' comments is sometimes allowed, but you should exercise caution in doing so."

As I've mentioned, I believed I did exercise due caution.

The tone of this statement in the guide does not at all reject (even as loudly) the changes that I made and the Wikipedia ethic as a whole may look down on yours.

The first (and, I assume, most important) 'guiding condition' they go on to list on that page is, "If you have their permission".

But I was correct by two other conditions in the article:

* Deleting material not relevant to improving the article

* You may redact (replace with a note, or collapse) large code samples once discussion of the sample has ended

In this light, what I did can in no way be compared to "vandalism", and actually goes along with the guidelines and purpose of the site.

The stuff I deleted was either outdated, irrelevant or had concluded in other ways.

Archiving may have been a better idea. But starting yet another pointless and misguided discussion about it would have only confounded the problem. Ironic and almost humorous (but not at this level).

I'm sure you could get into little details and nitpick about the holy laws, but in the end, I thought I was doing a 'good' thing, and I don't think there's any denying that.

You don't need to reply to this, I would just hope that next time you'd not have such a knee-jerk reaction.

Yet another irony that I'm wasting my time discussing this when my intention was to save others'.

Consider this discussion concluded. ;)

121.210.170.141 (talk) 13:12, 18 November 2009 (UTC)

You obviously completely misunderstand the way how Wikipedia talk pages operate, out-of-context quotes from the guideline notwithstanding. You have to familiarize yourself with the site before making such large-scale edits. Being outdated is not a valid reason to delete anything from the talk page. The vast majority of the sections you deleted were not irrelevant, and even if they were, such things are supposed to be deleted shortly after being posted, not several years afterwards. Collapsing large code samples has nothing to do with your edit, there are no code samples (or similar material) on the talk page. And so on. What you did is simply not the way things are done here. Wholesale deletions are typically considered vandalism. If as an inexperienced editor you intend to go around arguing with people who correct your mistakes instead of taking your lesson from them, you are heading for a big trouble. — Emil J. 13:37, 18 November 2009 (UTC)

Allllrighty then. "Will not do large scale deletions no matter how time-saving they seem." I'll write that on the black-board a hundred times. ;). Seriously: lesson learned, and even though it may have been questionable, I would have thought anybody who caught it would've let zealous rule-following go out the window after scrutinizing what was deleted and how old it was - if a tree falls in the forest. Thank god for your saintly behavior.... 121.210.170.141 (talk) 08:36, 20 November 2009 (UTC)

You should go ahead and delete or archive this conversation unless you think someone reading this page will learn from this convo. Disregarding my nagging, rest assured you've lit up the Tao of Wikipedia (maybe just with a small LED) for 1 of 6 billion other people. ;) (One small step at a time, I say - seriously wouldn't have known if that was a bad idea because everybody's thinking something along my line of thought, I assumed...)

While I'm here, I wonder if it'd be a good idea (consistent with mother Wikipedia) to turn some of the discussion sections into subsections of a larger section like "old"? —Preceding unsigned comment added by 121.210.170.141 (talk) 07:12, 22 November 2009 (UTC)

No, there is no reason to delete or archive this conversation, and no, it is not at all a good idea to mess with discussion sections. — Emil J. 16:06, 23 November 2009 (UTC)

IPA templates

Hi - what are the practical ramifications of not using the proper IPA templates? (Sorry if that's a silly question, I'm still getting to grips with all this.) I was attempting to preserve the technical help link, which I have been told is important to keep but is for some reason lost with the IPA-xx templates. Lfh (talk) 17:59, 8 December 2009 (UTC)

Using proper templates in general ensures that the same type of information is formatted the same way across different articles. In the particular case of IPA templates, it also simplifies automatic and semi-automatic maintenance (such as changes in the key, which seems to happen annoyingly often, or just checking that the transcriptions are correctly formed). If you think the help link is important, you should suggest on Template talk:Usage of IPA templates to add it in. — Emil J. 18:08, 8 December 2009 (UTC)

OK. A while ago I changed a generic audio/IPA template to IPA-en, and was reverted by an admin because my edit removed the help link. I discussed it with him and he raised the issue at Template talk:IPA-en, but it seemed to fall on deaf ears. Would Template talk:Usage of IPA templates have been a better place for him to discuss it? What about Template talk:IPA and Template talk:IPA-all, or are they for something else? There seems to be a conflict of needs between IPA links and audio help links, and it's well beyond my technical powers to help, but I hope at least the right people can be notified. Thanks for your help - Lfh (talk) 19:24, 8 December 2009 (UTC)

I think that Template talk:Usage of IPA templates is indeed a better place, it seems to be the usual venue for discussion of issues affecting all the IPA-xx templates. — Emil J. 12:55, 9 December 2009 (UTC)

Would you check something?

Greetings, I am going to attempt to improve the Rory Gallagher biography here. There was (until a couple weeks ago) an awful non-IPA rendering of his name, and another editor (upon request) placed a guess there which is an improvement, but I wonder if you might take a look at it-- are you familiar with the Irish language? I'd just like to be sure it's correct. Thanks. --Leahtwosaints (talk) 22:36, 12 December 2009 (UTC) Oh, almost forgot, while I'm at it-- anybody here you know who can place both Japanese and the IPA pronunciation of Keisuke Kuwata, a Blues rock musician from Japan that covers a lot of Western rock, blues, and folk music along with his own compostions in Japanese? --Leahtwosaints (talk) 23:36, 12 December 2009 (UTC)

The pronunciation in the Rory Gallagher article looks plausible, but I wouldn't really know. For both questions, you can try asking at the Language Reference Desk. — Emil J. 12:35, 14 December 2009 (UTC)

RDL troll

Hi. I must disagree with your restoration of the "Proto-Slavic thread" initiated by the RDL troll (84.62.***.***). The question was not genuine, and was intended only to disrupt. I know Angr and Ausoes are experienced wikipedians, but they fell for the trick, and they weren't the only ones; he still manages to get away with it ( see Mr. Bishi nonsense). Deletion of the trolling is not my invention; it's a common practice per WP:DENY. Please see [5] (esp. the end of the diff), or [6]. I know you restored it in the best possible faith, but I don't think it was the wisest cause of action. Regards, No such user (talk) 14:43, 8 January 2010 (UTC)

What makes you so certain that this particular question "was not genuine, and was intended only to disrupt"? WP:AGF. The question looks reasonable to me, and I don't see anything disruptive going on in that section. I understand that this is the same person who asked all the "why can't *... be a word of ..." questions, which were indeed quite annoying, nevertheless s/he also asks more sensible questions on phoneme distribution. If people are willing to answer the question, and others may be interested in seeing the answer, then I do not see the point of removing it; the question is not responsible for other actions of the questioner, if I may put it like this. Note also that WP:DENY which you keep referring to (1) is not a guideline or policy, but an essay, and (2) is targeted on vandalism, not trolling. — Emil J. 15:26, 8 January 2010 (UTC)

Deletion tag notification template

Hi Emilj, I noticed you put such a template on Qaedtgujol's talk page. I wanted to do the same for his article Square root of -i, but couldn't find the proper template. Can you give me a hint? Thanks & cheers, DVdm (talk) 14:02, 12 January 2010 (UTC)

When you put a speedy deletion template on a page, the template itself displays a suggestion as to what to put on the author's talk page. In your case it appears to be "{{subst:nn-warn-reason|Square root of -i|header=1|of the non-notability of the subject}} ~~~~" (though the last parameter might require some editing, I guess). — Emil J. 14:19, 12 January 2010 (UTC)

Indeed, I just found the template by looking at your edit. I will have at look at that parameter. Thanks. DVdm (talk) 14:23, 12 January 2010 (UTC)

Hereditary set

Thanks for your answer about hereditary sets in non-well-founded set theories. I'd greatly appreciate it if you could update the hereditary set article appropriately to reflect this. I'm afraid I'm outside my area of competence here. -- The Anome (talk) 15:20, 15 January 2010 (UTC)

Thank you! -- The Anome (talk) 16:17, 15 January 2010 (UTC)

Roth's Theorem

I was wondering about your edit in the article Thue-Siegel-Roth theorem. You claim that it is irrelevant whether p and q can be coprimes. Why so? I think that it is important, so that solutions of the form np/nq don't count, and make the statement that there are infinitely many solutions vacuously true. —Preceding unsigned comment added by Tercer (talk • contribs) 00:37, 5 February 2010 (UTC)

Consider a solution p,q, i.e.,

$\left|\alpha -{\frac {p}{q}}\right|<{\frac {1}{q^{2+\epsilon }}}.$

Now, replace it with np,nq. You obtain

$\left|\alpha -{\frac {np}{nq}}\right|<{\frac {1}{q^{2+\epsilon }}},$

but not necessarily

$\left|\alpha -{\frac {np}{nq}}\right|<{\frac {1}{(nq)^{2+\epsilon }}},$

so there is no reason why it should be a solution. In fact,

$\lim _{n\to \infty }{\frac {1}{n^{2+\epsilon }}}=0,$

therefore for any given p,q there are only finitely many n such that np,nq is a solution. Thus the two statements are equivalent. — Emil J. 11:26, 5 February 2010 (UTC)

Oh, indeed. Thanks. I wonder if it is worth to say this explicitly in the article, for greater clarity. Tercer (talk) 23:32, 5 February 2010 (UTC)

About Finland

On the Visa Policy of Canada map, you forgot to color Finland as a country with visa free access to Canada. —Preceding unsigned comment added by Couki (talk • contribs) 19:39, 13 February 2010 (UTC)

You see, I'm not the original author of the image. Anyway, I fixed Finland (and Greenland, which apparently shares visa non-requirements with Denmark).—Emil J. 11:04, 15 February 2010 (UTC)

Thank you for your response at the help desk.

How about the term "arithmetical formula" - for a formula all of whose function variables (and predicate variables) aren't quantified?

Another question:

Let's say we would like to formulate a bijection (or rather: a permutation) - from the class of invertible functions - to itself. So we can take: X - to be a free function-variable [or to be a function symbol] representing any invertible function, and Y - to be a free function-variable [or to be a function symbol] representing X's inverse function. Thus, we can build a bijection defined by the following trivial formula:

"∀a ((X(a)=X(a) → Y(X(a))=a) ∧ (Y(a)=Y(a) → X(Y(a))=a))".

(i.e. "for every a: if X is defined for a, then Y returns a for what's returned by X for a; and if Y is defined for a, then X returns a for what's returned by Y for a)".

Note that this formula involves a quantification over individual-variables only, not over function-variables: All of function variables [if any] are free here - as one should expect, since this formula is intended to define a correspondence (bijection), rather than a proposition.

My question is: how should we technically classify - by a common term - the logical language in which this formula is formulated (first order language? second order language? language with pure identity? arithmetical language?), while we would like to assume that this formula is formulated in the "minimal simplest" language needed for building this formula.

P.S. I also left another massage at the reference desk, regarding your first response.

Thank you in advance,

HOOTmag (talk) 20:19, 17 February 2010 (UTC)

Note that X(a) = X(a) is always true, both function variables and function symbols are assumed to be interpreted by total functions under the usual semantics. Which is a good thing, since a bijection and its inverse are also total by definition. Thus the formula may be simply written

$\forall a\,(X(Y(a))=a\land Y(X(a))=a).$

Now, whether it is a first-order or second-order formula, and in what language, depends on how you read it.

If you read X, Y as function variables, then it is a second-order formula in the empty language (aka language of pure equality). A model (in the full second-order semantics) of this language is just a nonempty set M; in order to find the truth value of the formula, you must give a valuation of its free variables, which amounts to assigning to X and Y particular functions from M to M. The formula will be true under this variable assignment if and only if the functions assigned to X and Y are mutually inverse bijections.

If, on the other hand, you read X, Y as function symbols, then the formula is a first-order sentence in the language $\langle X,Y\rangle$. A model of this language is a nonempty set equipped with two unary functions, and the sentence is true in the model if and only if the functions are mutually inverse bijections.

As you can see, the difference between the two is just cosmetic. Syntactically, they are essentially indistinguishable (barring some convention on what letters are function variables and what letters are function symbols). Semantically, the difference is whether the pair of functions we want to talk about is part of the model, or valuation of variables. Which of them is simpler is up to you.—Emil J. 14:31, 18 February 2010 (UTC)

Thank you again.

How about the term "arithmetical formula" - for a formula none of whose function variables (and predicate variables) are quantified? HOOTmag (talk) 14:56, 18 February 2010 (UTC)

This term is only adequate in the language of arithmetic, as Carl mentioned. For another context-dependent term, in the von Neumann–Bernays–Gödel set theory these formulas are called "normal". Technically, your formula does not use any nonlogical symbols, therefore it is indeed a formula both in the arithmetical language and in the language of set theory. However, calling it an arithmetical or normal formula would be highly misleading unless you want to apply it only in models of arithmetic or models of set theory, respectively.—Emil J. 15:16, 18 February 2010 (UTC)

1. Is the term "arithmetical formula" used also for formulae containing nonlogical symbols?
2. Let's assume that the context of the formula: "∀a ((Y(X(a))=a) ∧ (X(Y(a))=a))" is mathematical, i.e. the domain of discourse is the class of numbers. In this context, I need a proffessional term for exhausting the simplicity of that formula, e.g. by saying that "its (second order) language is empty", or even that it: "has only type 0 quantifiers and its (second order) language is empty", and the like. What would you suggest?

HOOTmag (talk) 16:30, 18 February 2010 (UTC)

Ad 1: yes, it is used for formulas in the language of arithmetic (0, S, +, ×, ≤, and possibly other symbols). Ad 2: I'm not quite sure I understand what you are after. I don't think there is a concise term describing the properties of the formula, just list them: "a second-order universal formula without second-order quantifiers and nonlogical symbols" (universal referring to the fact that it consists of a bunch of universal quantifiers (only one of them here, really) followed by an open formula). I don't know what do you want to do with the formula, but if you want to demonstrate its simplicity, it might be easiest just to show the formula explicitly.—Emil J. 19:00, 18 February 2010 (UTC)

Thank you again. I want to display this formula and then to claim that it's "simple" (regardless of its length); however, the word "simple" is not clear enough and needs clarification, and that's why I'd like to add more details describing its "simplicity", so - according to your suggestion - I can now say that it's a "formula without higher-order quantifiers and without nonlogical symbols", right? and how about a "formula, all of whose quantifiers are of first order, and whose (second order) language is empty"? HOOTmag (talk) 19:18, 18 February 2010 (UTC)

"...whose language is empty" sounds rather clumsy. Usually one does not talk about the language "of a formula", but the other way round: you first fix the language and this defines the set of possible formulas, you don't extract the language ex post from a formula.—Emil J. 13:44, 19 February 2010 (UTC)

Big O notation

I made a first step at fixing a perceived problem in the section Equals sign on the page for Big O notation a couple of days ago, which you have reverted. As far as I understand it, this subsection is about the abuse of notation involved in using the equals sign in statements such as f(x) = O(x²). The equals sign conventionally represents equality, which is an equivalence relation, and which is thus symmetric; and so if a = b then b = a. But this is exactly what is not true of an expression such as f(x) = O(x²), since O(x²) ≠ f(x). This is the problem discussed as that of "one-way equalit[ies]" on pp. 432–3 of Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete mathematics, 1st ed. (Addison-Wesley, 1989). (The same material seems to be on pp. 446–7 of the 2nd ed., according to Google Books.)

This subsection does start off by discussing this but then changes to discussing "the property of being O(g(x))" and claims that this is not symmetric (with a link to the page for symmetric relation). But this is a property, not a relation, and further very few (if any?) properties are "symmetric" in this sense (since for a function or property f(x) to be symmetric in this sense would imply something like, that for all functions g(x), if x = f(g(x)) then g(x) = f(x), assuming I've kept all that straight.)

The following text, about the "symbol" f(x), is irrelevant to the discussion here, so far as I can see, though it is a valid point about that notation. Then the final paragraph reverts to the initial subject of this subsection, that these are "one-way equalities", with a reference to another work by Knuth.

This is probably far too long as a comment about this on your talk page, and my apologies for that, but I'm still finding my feet here on Wikipedia. Would it okay if I were to re-write this subsection to match the description given in, for example, Concrete Mathematics or have I misunderstood what this section is trying to show?

Many thanks for your time. —Syncategoremata (talk) 01:53, 23 February 2010 (UTC)

The point being made by the example is that f(x) = O(g(x)), as a binary relation between functions f and g, is not symmetric. There are plenty of properties symmetric in this sense, such as plain equality. The version you replaced it,

x = O(x²) but O(x²) ≠ x,

does not make any sense: first, it is an invalid notation, as O is only allowed on the right-hand side of an equality, and second, if we allow such extension of the notation then the only sensible way of defining O(g(x)) = f(x) is to make it equivalent to f(x) = O(g(x)), rendering your statement wrong. I'm not convinced that non-symmetry of the "being O of" relation is relevant to the discussion of O as an abuse of notation, you have a point there, but it has to be fixed in a different way.—Emil J. 11:05, 23 February 2010 (UTC)

Many thanks for responding to this. There seem to be various issues with this subsection, some of which I think remain in your edited version.

You say in your comment above that "O is only allowed on the right-hand side of an equality", which has to be wrong: see that page's section on Complex usages, where O is used on both sides of an equation, as well as many examples in the works referenced in this section.

You also say that O is "a binary relation between functions", which again cannot be the case. As Knuth puts it "the notation O(g(n)) [stands] for the set of all functions f(n) such that |f(n)| ≤ C|g(n)| for some constant C" (Concrete Mathematics, 1st ed., p. 432). De Bruijn makes a similar point on p. 6 of his work referenced on that page.

This returns us to my initial point about this being an issue of the symmetry of equality, which I believe is the central point. I've edited this subsection in an attempt to fix these issues and added some quotes and references to both Knuth and de Bruijn in an attempt to explain this.

Also, as I mentioned in my first comment, this claim:

The symbol f(x) means the value of the function f for the argument x, the symbol for the function itself is f rather than f(x).

seems to be irrelevant to the issue. It's also not true: as you can see in the quote from Knuth above, mathematicians are perfectly happy to use an expression such as f(x) to refer to a function, as well as using it to refer to a particular value of a function. Thus I've removed this part entirely.

So as I mentioned, I've changed this subsection in an attempt to fix some of these issues. Please do you respond if you are not happy with what I've done. Many thanks –Syncategoremata (talk) 18:39, 23 February 2010 (UTC)

Thank you for your effort to help me

What I see now is דּ͏ָוִד and שׁ͏ִמְעוֹן‎, i.e. I see a square ͏ in front of the vowel-sign that is under the first letter.

Following our other discussion, just tell me if you think that my last question (ibid.) seems to need stronger tools than those you are familiar with. The question was as follows: Let S be the set of all polynomials f,g. Note that each one of the function-symbols f,g is to be interpreted as a polynomial. Now, how can we prove the impossibilty of surjecting / injecting from S to itself, by a first order formula which can be formulated in every language of any structure of the form $\langle \mathbb {R} ,f,g\rangle$, when ignoring the trivial identity bijection - which of course can be induced by the formula (x)(f(x)=g(x))? HOOTmag (talk) 12:14, 15 March 2010 (UTC)

It sounds like something which should be possible to do relatively easily with standard techniques, maybe with some tweaking. But it's a quite unusual setup, I would have to think about it more and I don't have the time for that right now.—Emil J. 13:22, 16 March 2010 (UTC)

Ok, take your time. Anyways, thanks a lot for your help up to now. I appreciate that.

Additionally, note that my question about the polynomials is just an example, and I'll welcome any simpler example of impossibility of surjecting / injecting from a given set F to a given set G (provided that the functions f,g are total, and the sets F,G have the same cardinality, or any cardinality which permits the very surjection/injection).

HOOTmag (talk) 13:36, 16 March 2010 (UTC)

Actually, I think that $f\mapsto f^{(3)}$ (that's iteration, not derivative) is a definable injection of polynomials to themselves.—Emil J. 15:14, 16 March 2010 (UTC)

Interesting conjecture. If it's true then my question about the polynomials will refer to surjections only. HOOTmag (talk) 16:48, 16 March 2010 (UTC)

Update for Diplomatic Missions of Kosovo map

Kosovo has opened embassies in the Czech Republic, Japan and Macedonia. Could you please update the map? I've no idea how to do it. Thanks! - Canadian Bobby (talk) 22:39, 20 March 2010 (UTC)

OK, done.—Emil J. 10:25, 22 March 2010 (UTC)

BPP

Nice catch here [7]. Thanks! I mistakenly thought that P not equal to BPP implied a collapse. --Robin (talk) 14:47, 22 March 2010 (UTC)

Thanks for your edits to Sinc function.

I thought that I might clean up that product notation as you did, but I wasn't sure what the motivation was for expressing it more as the limit in the first place. Also I didn't even know that one identity originally ascribed to Euler, let alone who to credit it to. 71.169.190.178 (talk) 19:13, 15 April 2010 (UTC)

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