This notion is used, for example, in " Chain (algebraic topology)", with a link to " Free abelian group"; there, "formal sums" are defined (but "formal linear combinations" are not). In some books I see "formal linear combinations" used with no definition (and often, with no explanation). Once I used it on an undergraduate lecture and was asked by students: "what's it?"
Should we redirect "Formal linear combination" to "Free abelian group"? Should we enlarge the latter, including non-integer coefficients? Boris Tsirelson ( talk) 17:27, 31 May 2015 (UTC)
I have rewritten the corresponding section of Free module for defining explicitly formal linear combination (and also for being less technical). I have also created the redirect Formal linear combination. D.Lazard ( talk) 09:17, 1 June 2015 (UTC)
Please take a look at mathematical logic. -- Trovatore ( talk) 18:30, 26 May 2015 (UTC)
Sorry that I missed this debate :-) -- GodMadeTheIntegers ( talk) 18:00, 2 June 2015 (UTC)
Much weakened version of that lemma is formulated in our article. The reason (articulated on the talk page) is that the simple proof given in the article does not give more. As for me, irrespective of the proof, a stronger formulation should be given. But for now I have only lecture notes as sources. I wonder, do you know better sources? Mine are:
Boris Tsirelson ( talk) 11:53, 29 May 2015 (UTC)
See theorems 1.2.4 and 1.2.5 in volume 1 of Hörmander. If f is a continuous (resp. locally integrable) function st for all compactly supported smooth φ
then f=0 (resp f=0 a.e.) Sławomir Biały ( talk) 16:47, 29 May 2015 (UTC)
There is an ongoing and somewhat agitated discussion of the Poincare conjecture here. Tkuvho ( talk) 13:37, 3 June 2015 (UTC)
The page on the Vietoris–Rips complex lacks a formal definition written in a readable format. Please fix thanks. — Preceding unsigned comment added by 98.223.78.42 ( talk) 14:40, 3 June 2015 (UTC)
Currently Lagrange's method redirects to Lagrange multiplier, but apparently in the world of PDE's, Lagrange's method means something entirely different. For example, see [3]. Do we cover the PDE meaning of Lagrange's method? Is seems like if it's anywhere it would be in First-order partial differential equation but I didn't see it in recognizable form, though it's not my area of expertise. -- RDBury ( talk) 12:20, 4 June 2015 (UTC)
I notice a set of mass changes to some articles. -- Ancheta Wis (talk | contribs) 04:57, 7 June 2015 (UTC)
This may be of interest to those on this talk page: as I stated at Wikipedia talk:WikiProject Physics#Status of new article Complex spacetime, this new article might need some broader scrutiny. — Quondum 14:18, 10 June 2015 (UTC)
Conjugacy-closed subgroup is an orphaned article: no other articles link to it. Michael Hardy ( talk) 23:22, 10 June 2015 (UTC)
Opine on a proposed deletion at Wikipedia:Articles for deletion/Quaternion rotation biradial. Michael Hardy ( talk) 17:34, 14 June 2015 (UTC)
It seems that some of the links to PM in Wikipedia articles are not working. For example, the following link [4] in the article Hartogs' theorem is not working. It was added using the Template:PlanetMath attribution. New link seems to be [5]. Also the link [6] in Ancient Egyptian multiplication does not work. The new link is [7]. This probably influences many articles (and templates). What ca be done with it? Can this be resolved automatically, or is manual change the only way to go? -- Kompik ( talk) 08:03, 15 June 2015 (UTC)
[
http://planetmath.org/encyclopedia/{{{urlname}}}.html
[
http://planetmath.org/{{{urlname}}}
We seem to have no article on quotient structures in general. We have Quotient (disambiguation), which lists a bunch of things as if they were different things known by the same name, with no idea common to all of them. Should we have a quotient structure article? Michael Hardy ( talk) 18:18, 15 June 2015 (UTC)
Is there deletion sorting for mathematics-related articles or do they just end up under Wikipedia:WikiProject Deletion sorting/Science?
Anyway there are three articles at AfD about algorithms for voting systems, not sorted into anything technical:
Thanks for looking at these. StarryGrandma ( talk) 23:05, 19 June 2015 (UTC)
At Wikipedia:WikiProject Mathematics/Current activity, we find no new articles since May 25. Jitse's bot, run by Jitse Niesen, which edits that page, has done so more recently, and mathbot, which, among other things, lists new articles, whose lists are used by Jitse's bot, has been active more recently. Are there no new articles? Michael Hardy ( talk) 18:44, 31 May 2015 (UTC)
I'm experiencing the same problem described by user Michael Hardy... Currently, the last date I can see on the "New articles:" section on the table is "5 Jun". But there were indeed mathematical articles created after 5 Jun ( Yair Minsky (6 Jun) and Richard Canary (7 Jun) are proof of this). — Preceding unsigned comment added by 189.6.195.23 ( talk) 13:24, 8 June 2015 (UTC)
The bot has been having problems on and off for a couple of months. See the last two sections of User talk:Jitse's bot. I've tried pinging and e-mailing Jitse Niesen but have had no response. I don't know if there's anything else that can be done, such as someone else take over maintaining them.-- JohnBlackburne words deeds 13:32, 8 June 2015 (UTC)
Are Dependence relation and Dependency relation the same thing? WhatamIdoing ( talk) 03:13, 22 June 2015 (UTC)
Hi there.
Over at Wikipedia:Redirects_for_discussion/Log/2015_June_20#Category_of_graded_vector_spaces this has been listed. I think it is redundant and perhaps harmful since it is not a Wikipedia catgegory but a redirect to an article: surely the grading/graduation is itself the way to categorise them so to categorise the grading would be some higher order function, which I'm sure is not intended here. (To categorise the categorisation, i.e. in formal logic of some kind, Bertie Russell turning in his grave).
I only have maths up to basic graduate degree level, and mostly on the engineering side of it rather than theory, so I'd appreciate your opinion on whether this is useful. Si Trew ( talk) 07:22, 22 June 2015 (UTC) see my userpage on 3d slope formula here — Preceding undated comment added 00:34, 23 June 2015 (UTC)
I am in the process of renaming two-letter filenames on Commons, to provide less ambiguous titles. Today I came across this one:
What is this equation? Or, more directly, what would be an appropriately unambiguous, but concise, name for this image file? Cheers! bd2412 T 19:55, 24 June 2015 (UTC)
The book The Assayer by Galileo is one of the works that ushered in the scientific method as well as the method of indivisibles closely related to Galileo's atomism. Recently I added sourced material on this aspect of the book. Input would be appreciated. Tkuvho ( talk) 07:36, 25 June 2015 (UTC)
An editor has asked for a discussion to address the redirect Dualizing sheaf. Please participate in the redirect discussion if you have not already done so. Ivanvector ( talk) 14:48, 25 June 2015 (UTC)
A new copy-paste detection bot is now in general use on English Wikipedia. Come check it out at the EranBot reporting page. This bot utilizes the Turnitin software (ithenticate), unlike User:CorenSearchBot that relies on a web search API from Yahoo. It checks individual edits rather than just new articles. Please take 15 seconds to visit the EranBot reporting page and check a few of the flagged concerns. Comments welcome regarding potential improvements. These likely copyright violations can be searched by WikiProject categories. Use "control-f" to jump to your area of interest.-- Lucas559 ( talk) 22:25, 25 June 2015 (UTC)
The word "metric" is used differently in (1) the context of a metric space, and (2) such context as "the metric of space-time".
Thus, sometimes a space endowed with a metric is not a metric space. Regretfully, this confusing situation is not explained enough in our articles. See the ongoing dispute: Talk:Metric space#Questions to User:Verdana Bold about a recent attempt to emphasize the "more physical" usage of the word "metric". Indeed, that usage is notable and should be mentioned. However, this should be made carefully enough. Boris Tsirelson ( talk) 17:35, 27 June 2015 (UTC)
There is a silly argument going on between myself and two other editors at the new article real projective line about whether "really" is a circle. At first, it was argued that it must be homeomorphic but not diffeomorphic to a circle, because the universal cover of is , and that of is , and the property of being one's own universal cover is a diffeomorphism invariant - fortunately this argument was dropped. Then it was argued that it may be topologically equivalent to a circle, but have a different geometric structure, but later it was accepted that the natural metric makes isometric to a circle. Presently it is argued (I think) that there is some intermediate structure, stronger than the topological structure but weaker than the metric space structure, wherein cross-ratios of four points can be defined without reference to any distance function. I believe this is impossible; defining the cross-ratio (and proving that it is well-defined) requires using the metric. The reason this is significant is that I believe it is important to state clearly in the lede that the object is a circle, without reference to terminology that may confuse laymen, such as "homeomorphic," "isometric," or "birationally equivalent." This is the text I want:
In mathematics, the real projective line is a circle. It is a trivial example of a more general class of topological spaces known as projective spaces. The real projective line is formed from lines through the origin in two-dimensional space. One considers these lines to be the "points" of the real projective line, and the angle between them to be the "distance" between these "points." Formally, the lines through the origin form equivalence classes, allowing for the real projective line to be defined as a quotient space.
Having this context in mind may give the reader a better chance of understanding the technical details that follow. I think the importance of stating clearly that we are talking about nothing other than a complicated way to define a circle is shown by the talk page itself. Even a relatively mathematically-sophisticated reader might see "a space homeomorphic to a circle" and think that it has some other geometric structure, that it is a double cover of a circle, or whatever. This is what led a normally quite competent editor to the logical and factual fallacies in the "homeomorphic but not diffeomorphic" argument above; he was trying too hard to rationalize a wrong idea, when the truth was just too simple. On a related note, the article is also suffering from the idea that the group is the "automorphism group" of the real projective line. I think that someone just made this up. It is now the central principle in the platform of the "not a circle" party. -- Sammy1339 ( talk) 13:49, 26 June 2015 (UTC)
@Sammy : If one defines distance between two points on a circle to be the length of the chord between them, then that is topologically but not metrically equivalent to the circle intrinsic metric in which the distance is the arc length. Might that be the circle that is not isomorphic to the projective line, or is the chord-length metric a natural thing to use for that? As far as cross-ratios go, linear fractional transformations on the complex numbers take circles to other circles while changing distances but leaving cross-ratios intact. Therefore the function assigning cross-ratios to quadruples of points on the circle does not determine the function assigning distances between them. In that sense one can say that the cross-ratio function amounts to less structure than the metric but more than the topology. Michael Hardy ( talk) 23:41, 26 June 2015 (UTC)
I would also like to suggest that at some point someone makes an attempt to find sources supporting their position, rather than relying on appeals to pure reason only. (And that is the last from me, probably.) -- JBL ( talk) 01:15, 27 June 2015 (UTC)
This notion is used, for example, in " Chain (algebraic topology)", with a link to " Free abelian group"; there, "formal sums" are defined (but "formal linear combinations" are not). In some books I see "formal linear combinations" used with no definition (and often, with no explanation). Once I used it on an undergraduate lecture and was asked by students: "what's it?"
Should we redirect "Formal linear combination" to "Free abelian group"? Should we enlarge the latter, including non-integer coefficients? Boris Tsirelson ( talk) 17:27, 31 May 2015 (UTC)
I have rewritten the corresponding section of Free module for defining explicitly formal linear combination (and also for being less technical). I have also created the redirect Formal linear combination. D.Lazard ( talk) 09:17, 1 June 2015 (UTC)
Please take a look at mathematical logic. -- Trovatore ( talk) 18:30, 26 May 2015 (UTC)
Sorry that I missed this debate :-) -- GodMadeTheIntegers ( talk) 18:00, 2 June 2015 (UTC)
Much weakened version of that lemma is formulated in our article. The reason (articulated on the talk page) is that the simple proof given in the article does not give more. As for me, irrespective of the proof, a stronger formulation should be given. But for now I have only lecture notes as sources. I wonder, do you know better sources? Mine are:
Boris Tsirelson ( talk) 11:53, 29 May 2015 (UTC)
See theorems 1.2.4 and 1.2.5 in volume 1 of Hörmander. If f is a continuous (resp. locally integrable) function st for all compactly supported smooth φ
then f=0 (resp f=0 a.e.) Sławomir Biały ( talk) 16:47, 29 May 2015 (UTC)
There is an ongoing and somewhat agitated discussion of the Poincare conjecture here. Tkuvho ( talk) 13:37, 3 June 2015 (UTC)
The page on the Vietoris–Rips complex lacks a formal definition written in a readable format. Please fix thanks. — Preceding unsigned comment added by 98.223.78.42 ( talk) 14:40, 3 June 2015 (UTC)
Currently Lagrange's method redirects to Lagrange multiplier, but apparently in the world of PDE's, Lagrange's method means something entirely different. For example, see [3]. Do we cover the PDE meaning of Lagrange's method? Is seems like if it's anywhere it would be in First-order partial differential equation but I didn't see it in recognizable form, though it's not my area of expertise. -- RDBury ( talk) 12:20, 4 June 2015 (UTC)
I notice a set of mass changes to some articles. -- Ancheta Wis (talk | contribs) 04:57, 7 June 2015 (UTC)
This may be of interest to those on this talk page: as I stated at Wikipedia talk:WikiProject Physics#Status of new article Complex spacetime, this new article might need some broader scrutiny. — Quondum 14:18, 10 June 2015 (UTC)
Conjugacy-closed subgroup is an orphaned article: no other articles link to it. Michael Hardy ( talk) 23:22, 10 June 2015 (UTC)
Opine on a proposed deletion at Wikipedia:Articles for deletion/Quaternion rotation biradial. Michael Hardy ( talk) 17:34, 14 June 2015 (UTC)
It seems that some of the links to PM in Wikipedia articles are not working. For example, the following link [4] in the article Hartogs' theorem is not working. It was added using the Template:PlanetMath attribution. New link seems to be [5]. Also the link [6] in Ancient Egyptian multiplication does not work. The new link is [7]. This probably influences many articles (and templates). What ca be done with it? Can this be resolved automatically, or is manual change the only way to go? -- Kompik ( talk) 08:03, 15 June 2015 (UTC)
[
http://planetmath.org/encyclopedia/{{{urlname}}}.html
[
http://planetmath.org/{{{urlname}}}
We seem to have no article on quotient structures in general. We have Quotient (disambiguation), which lists a bunch of things as if they were different things known by the same name, with no idea common to all of them. Should we have a quotient structure article? Michael Hardy ( talk) 18:18, 15 June 2015 (UTC)
Is there deletion sorting for mathematics-related articles or do they just end up under Wikipedia:WikiProject Deletion sorting/Science?
Anyway there are three articles at AfD about algorithms for voting systems, not sorted into anything technical:
Thanks for looking at these. StarryGrandma ( talk) 23:05, 19 June 2015 (UTC)
At Wikipedia:WikiProject Mathematics/Current activity, we find no new articles since May 25. Jitse's bot, run by Jitse Niesen, which edits that page, has done so more recently, and mathbot, which, among other things, lists new articles, whose lists are used by Jitse's bot, has been active more recently. Are there no new articles? Michael Hardy ( talk) 18:44, 31 May 2015 (UTC)
I'm experiencing the same problem described by user Michael Hardy... Currently, the last date I can see on the "New articles:" section on the table is "5 Jun". But there were indeed mathematical articles created after 5 Jun ( Yair Minsky (6 Jun) and Richard Canary (7 Jun) are proof of this). — Preceding unsigned comment added by 189.6.195.23 ( talk) 13:24, 8 June 2015 (UTC)
The bot has been having problems on and off for a couple of months. See the last two sections of User talk:Jitse's bot. I've tried pinging and e-mailing Jitse Niesen but have had no response. I don't know if there's anything else that can be done, such as someone else take over maintaining them.-- JohnBlackburne words deeds 13:32, 8 June 2015 (UTC)
Are Dependence relation and Dependency relation the same thing? WhatamIdoing ( talk) 03:13, 22 June 2015 (UTC)
Hi there.
Over at Wikipedia:Redirects_for_discussion/Log/2015_June_20#Category_of_graded_vector_spaces this has been listed. I think it is redundant and perhaps harmful since it is not a Wikipedia catgegory but a redirect to an article: surely the grading/graduation is itself the way to categorise them so to categorise the grading would be some higher order function, which I'm sure is not intended here. (To categorise the categorisation, i.e. in formal logic of some kind, Bertie Russell turning in his grave).
I only have maths up to basic graduate degree level, and mostly on the engineering side of it rather than theory, so I'd appreciate your opinion on whether this is useful. Si Trew ( talk) 07:22, 22 June 2015 (UTC) see my userpage on 3d slope formula here — Preceding undated comment added 00:34, 23 June 2015 (UTC)
I am in the process of renaming two-letter filenames on Commons, to provide less ambiguous titles. Today I came across this one:
What is this equation? Or, more directly, what would be an appropriately unambiguous, but concise, name for this image file? Cheers! bd2412 T 19:55, 24 June 2015 (UTC)
The book The Assayer by Galileo is one of the works that ushered in the scientific method as well as the method of indivisibles closely related to Galileo's atomism. Recently I added sourced material on this aspect of the book. Input would be appreciated. Tkuvho ( talk) 07:36, 25 June 2015 (UTC)
An editor has asked for a discussion to address the redirect Dualizing sheaf. Please participate in the redirect discussion if you have not already done so. Ivanvector ( talk) 14:48, 25 June 2015 (UTC)
A new copy-paste detection bot is now in general use on English Wikipedia. Come check it out at the EranBot reporting page. This bot utilizes the Turnitin software (ithenticate), unlike User:CorenSearchBot that relies on a web search API from Yahoo. It checks individual edits rather than just new articles. Please take 15 seconds to visit the EranBot reporting page and check a few of the flagged concerns. Comments welcome regarding potential improvements. These likely copyright violations can be searched by WikiProject categories. Use "control-f" to jump to your area of interest.-- Lucas559 ( talk) 22:25, 25 June 2015 (UTC)
The word "metric" is used differently in (1) the context of a metric space, and (2) such context as "the metric of space-time".
Thus, sometimes a space endowed with a metric is not a metric space. Regretfully, this confusing situation is not explained enough in our articles. See the ongoing dispute: Talk:Metric space#Questions to User:Verdana Bold about a recent attempt to emphasize the "more physical" usage of the word "metric". Indeed, that usage is notable and should be mentioned. However, this should be made carefully enough. Boris Tsirelson ( talk) 17:35, 27 June 2015 (UTC)
There is a silly argument going on between myself and two other editors at the new article real projective line about whether "really" is a circle. At first, it was argued that it must be homeomorphic but not diffeomorphic to a circle, because the universal cover of is , and that of is , and the property of being one's own universal cover is a diffeomorphism invariant - fortunately this argument was dropped. Then it was argued that it may be topologically equivalent to a circle, but have a different geometric structure, but later it was accepted that the natural metric makes isometric to a circle. Presently it is argued (I think) that there is some intermediate structure, stronger than the topological structure but weaker than the metric space structure, wherein cross-ratios of four points can be defined without reference to any distance function. I believe this is impossible; defining the cross-ratio (and proving that it is well-defined) requires using the metric. The reason this is significant is that I believe it is important to state clearly in the lede that the object is a circle, without reference to terminology that may confuse laymen, such as "homeomorphic," "isometric," or "birationally equivalent." This is the text I want:
In mathematics, the real projective line is a circle. It is a trivial example of a more general class of topological spaces known as projective spaces. The real projective line is formed from lines through the origin in two-dimensional space. One considers these lines to be the "points" of the real projective line, and the angle between them to be the "distance" between these "points." Formally, the lines through the origin form equivalence classes, allowing for the real projective line to be defined as a quotient space.
Having this context in mind may give the reader a better chance of understanding the technical details that follow. I think the importance of stating clearly that we are talking about nothing other than a complicated way to define a circle is shown by the talk page itself. Even a relatively mathematically-sophisticated reader might see "a space homeomorphic to a circle" and think that it has some other geometric structure, that it is a double cover of a circle, or whatever. This is what led a normally quite competent editor to the logical and factual fallacies in the "homeomorphic but not diffeomorphic" argument above; he was trying too hard to rationalize a wrong idea, when the truth was just too simple. On a related note, the article is also suffering from the idea that the group is the "automorphism group" of the real projective line. I think that someone just made this up. It is now the central principle in the platform of the "not a circle" party. -- Sammy1339 ( talk) 13:49, 26 June 2015 (UTC)
@Sammy : If one defines distance between two points on a circle to be the length of the chord between them, then that is topologically but not metrically equivalent to the circle intrinsic metric in which the distance is the arc length. Might that be the circle that is not isomorphic to the projective line, or is the chord-length metric a natural thing to use for that? As far as cross-ratios go, linear fractional transformations on the complex numbers take circles to other circles while changing distances but leaving cross-ratios intact. Therefore the function assigning cross-ratios to quadruples of points on the circle does not determine the function assigning distances between them. In that sense one can say that the cross-ratio function amounts to less structure than the metric but more than the topology. Michael Hardy ( talk) 23:41, 26 June 2015 (UTC)
I would also like to suggest that at some point someone makes an attempt to find sources supporting their position, rather than relying on appeals to pure reason only. (And that is the last from me, probably.) -- JBL ( talk) 01:15, 27 June 2015 (UTC)