![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 |
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)
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)
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)
You're quite right - I was getting Afghanistan and Albania mixed up... Bazonka ( talk) 17:09, 16 July 2009 (UTC)
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)
![]() |
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) |
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)
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 ().
Svick (
talk)
09:56, 2 September 2009 (UTC)
VERY SORRY -- Factuarius ( talk) 16:32, 2 September 2009 (UTC)
Please don't mark non-minor edits as minor, like this one. See Help:Minor edit:
"When not to mark an edit as minor:
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)
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 such that has density .
Consider an equidistributed sequence in and define
Then, by definition, for all and for all . As a consequence, in any finite collection of , 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)
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 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)
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)
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)
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)
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(N1/2(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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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).
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 , 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)
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)
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)
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)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 |
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | Archive 4 |
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)
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)
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)
You're quite right - I was getting Afghanistan and Albania mixed up... Bazonka ( talk) 17:09, 16 July 2009 (UTC)
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)
![]() |
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) |
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)
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 ().
Svick (
talk)
09:56, 2 September 2009 (UTC)
VERY SORRY -- Factuarius ( talk) 16:32, 2 September 2009 (UTC)
Please don't mark non-minor edits as minor, like this one. See Help:Minor edit:
"When not to mark an edit as minor:
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)
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 such that has density .
Consider an equidistributed sequence in and define
Then, by definition, for all and for all . As a consequence, in any finite collection of , 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)
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 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)
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)
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)
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)
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(N1/2(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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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).
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 , 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)
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)
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)
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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