Talk:Glossary of mathematical jargon

message: I'm not sure I agree with all that is said. But in any case it might warrant an article. Charles Matthews 12:02, 11 Apr 2005 (UTC)
replies: text: An "In general" article would have no potential for becoming anything more than a dictionary definition.As such, it'll be tagged (rightfully imho) with  and then , merged back into here, and deleted or replaced with a redirect link. So don't bother. —msh210 03:39, 26 Apr 2005 (UTC)
thread_title: [[In general]]

message: I've given a new face to this page, since I found the old version to be sprawling, arbitrary, and rather ugly.  I've simply divided the terms into categories and given a broad overview of each category.  My next move will be to regularize the presentation of the page and add simple descriptions to each term.  Finally, a few terms landed in "Miscellaneous" for a few reasons: LHS/RHS is seemingly none of the above categories, "transport of structure" is a term I've never heard and has no page to describe it, and "wrt" is hardly specific to mathematics.  I think that the latter two ought to go, and if anyone could argue whether LHS/RHS belongs under Proof or Qualitative, or even Philosophical, it would be nice. Ryan Reich 00:29, 24 February 2006 (UTC)
replies: text: Wikipedia frowns on major edits to an article when there's an AFD discussion going on, since it confuses things, but your changes are so excellent that I don't think anybody will object. - DavidWBrooks 14:07, 24 February 2006 (UTC)
replies: text:  Not that almost anyone is objecting to the article at large, anyway.  Thanks. Ryan Reich 14:17, 24 February 2006 (UTC)

text: Not sure what general opinion would be, but if you go by Wikipedia:Guide to deletion, then it positively encourages editing an article during an AfD discussion, simply recommending that significant edits should be noted on the article's talk page (it does prohibit blanking, renaming or redirecting and strongly discourages merging during AfD). But we can certainly agree on the excellent quality of Ryan's edits - keep up the good work ! Gandalf61 14:44, 24 February 2006 (UTC)
replies: text: That's the trouble with having been on wikipedia too long - I learn things, then they go and get updated! I got yelled at for editing a then-VFD article ... but then again, that was 2003. - DavidWBrooks 16:05, 24 February 2006 (UTC)
thread_title:  Structural revision 

message: Somewhat related to the non-techniques, there are the invalid techniques, such as
* Proof by intimidation (As any idiot can see,...)
* Proof by lack of imagination
* Proof by example
* Proof by picture
Googling such terms reveals many others. Btyner 17:24, 5 September 2006 (UTC)
replies: text: These all remind me of a joke poster I saw up around school a year or two ago, which had a whole list of these together with suggested methods.  They're also self-explanatory and not specific to mathematics, really.  Some of them (especially "lack of imagination") could have a case made for being put in logical fallacies, though.  Actually, that one already is. Ryan Reich 22:25, 6 September 2006 (UTC)
thread_title:  some more 

message: How about frontier question?—msh210℠ 16:58, 7 December 2006 (UTC)
replies: text: How about it?  I don't know the term but others might. Ryan Reich 18:49, 7 December 2006 (UTC)
thread_title:  frontier question 

message: I'm sorry, I don't see why this is more accurate.  Can you even explain what this term (i.e. non-technique) means? The phrase furthermore strikes me as being excessively cute. .--CSTAR 18:56, 7 December 2006 (UTC)
replies: text: I also don't see why logical fallacies need to be mentioned here. --CSTAR 19:06, 7 December 2006 (UTC)
replies: text:  As for the fallacies, since someone thought it worth mentioning incorrectly it is at least worth mentioning correctly.  And now that I think about it, there is a point to be made that these terms are not logical fallacies, but simply bad form.  As for the terminology, I was first of all trying to write concise, efficient headings and this is the best I could do to convey that these terms: a) appear in proofs; b) purport to contribute to the proof; and c) in fact detract from it, or at least fail to constitute proper technique.  Hence, they are non-techniques.  Writing "Non proof techniques" is ugly, "Non-proof techniques" is just wrong since it suggests that they are techniques to do this imaginary "non-proof" thing, and omitting the term "technique" fails to make the connection with the previous section, which I think is important.  Your suggestion, "Other phrases appearing in proofs", is far too general since it doesn't mention that these are phrases (or strategies) that do not belong in proofs.  And yes, I wanted it to be sort of cute. Ryan Reich 18:32, 8 December 2006 (UTC)
replies: text:  They do not belong in proofs? The fact is they are in proofs appearing in papers, books as well as in the lecture hall.  To say they do not belong in proofs seems like a normative judgement about what constitutes a proof, which does not belong here, in my opinion. We are here, I believe not talking about proofs developed within some formal system. --CSTAR 19:35, 8 December 2006 (UTC)
replies: text:  Yes, they don't belong in formal proofs, but I chose the titles to reflect the reason I think underlies this, not the fact itself.  The question is still about technique: what differentiates these terms from the ones in "Proof techniques" is that those are methods of rigorous, albeit shorthanded argument, and these are at best guidelines to such an argument.  "WLOG" is to "clearly" as a model ship is to the box of parts with a picture on the cover.  That's the only distinction I'm trying to make: even someone who puts "clearly" in a proof knows he is being terribly informal, however accepted the proof might be as a result of the fact that people are not, after all, machines, and have the imagination to build the ship.  I'm not trying to make a judgement about what a proof is with my title; I'm just separating terms which are prescriptive from those which are descriptive.  However, while I was writing this I thought of a solution.  Let's call "Proofs and proof techniques" instead "Proofs and rigorous proof techniques", and the current "Proof non-techniques" instead "Informal proof technqiues".  We might want to call "Informalities" something like "Descriptive informalities" to distinguish it from informalities of argument, in this case. Ryan Reich 14:49, 9 December 2006 (UTC)
replies: text:  Though I think your suggestion is an improvement, I think there is still a problem here which results from the following: a mathematical proof  (in a lecture, or paper or book) isn't necessarily a sequence of inferences (say in a sequent calculus) or even an approximation to such an object, but is itself a higher order object -- in part, a recipe for constructing such a proof object or even more abstractly an argument why such a proof object exists (which could legimately include appeals to other principles, assumptions about the interlocutor's experience, even pictures). That is why there is all this jargon. The view of proof that is suggested here is too narrow in my opinion and does not adequately convey the flavor of mathematical communication.--CSTAR 15:23, 9 December 2006 (UTC)
replies: text:  Going by what you describe, it would seem there is no problem with calling them "informal proof techniques", since they are indeed tools for the informal proof-like communication that you mention.  Or are you saying that we should just put all the proof-related jargon into a single subsection? Ryan Reich 15:58, 9 December 2006 (UTC)
replies: text:  No I'm satisfied with the distinction you make. I'm just pointing out that an informal proof should not be thought of as a bad proof.--CSTAR 16:02, 9 December 2006 (UTC)
replies: text:  Oh, okay.  I'll make the changes, then. Ryan Reich 16:28, 9 December 2006 (UTC)
thread_title: Proof non-techniques 

message: I am not sure if that kind of comment is regarded as bad wikipedia-style (if so please feel free to delete it) but i just wanted to mention that for me the article was very insightful and valuable. It is not easy to find that kind of information in a standard introductionary text book about mathmatics although I think it would definitely belong there. Just wanted to thank the editors of this page for their work, highly appreciated.  —Preceding unsigned comment added by 130.88.179.123 (talk) 23:28, 3 June 2008 (UTC)
replies: text: Saying "thank you" is never bad style ! Glad you found the page useful. Gandalf61 (talk) 08:41, 4 June 2008 (UTC)
thread_title: quality of the text

message: In the context of limits, this is shorthand for arbitrarily large and its relatives; as with eventually, the intended variant is implicit. As an example, one could say that "The function sin(x) is frequently zero", where "frequently" means "for arbitrarily large x".
I strongly disagree.  If someone tells me a function is frequently zero I take them to mean, based on formality of the context, either: (a) the function vanishes infinitely often but not everywhere; or (b) the function vanishes more than once. 
--129.79.237.217 (talk) 15:57, 20 June 2008 (UTC)
replies: text: I'd ask for a citation, but I don't have one either :).  However, your usage (a) is the same as mine on the real line, except for "not everywhere", which is sort of a vacuous implication case; your second is perhaps new, though I've never heard the term used so loosely.  However, I don't much hear people talking about real functions these days, either.  The example is not very good, though; the usage I had in mind was more like "sin(x) has no limit at infinity because it is frequently equal to both 1 and -1".  But there's no point in my arguing; I wrote the current text based on my experience, and you have presented a new and different experience, which you can append to make the explanation more comprehensive.  One day I'd like to find books which say these things. Ryan Reich (talk) 16:49, 20 June 2008 (UTC)
replies: text: Mathematicians frequently disagree amongst themselves about the meaning of "frequently".  --Lambiam 22:25, 26 June 2008 (UTC)
replies: text:  True; however As an example, one could say that "The function sin(x) is frequently zero", where "frequently" means "for arbitrarily many x". would be closer to my understanding of the phrase.  yoyo (talk) 15:15, 2 July 2018 (UTC)
thread_title:  frequently 

message: This article lists a bunch of references but the ones I checked don't seem to connect with anything in the article. Many of the phrases are well known to mathematicians and so the definitions do not strictly need to be sourced, but the ones that are not common knowledge should have inline cites. Even for the common knowledge terms, it would be desirable to have a source where it is used.--RDBury (talk) 09:46, 3 April 2010 (UTC)
thread_title:  Referencing 

message: I think parts of this article need better sourcing. Many terms are described without references. Ulner (talk) 20:36, 24 July 2010 (UTC)
thread_title:  Improved sourcing 

message: What about adding "degenerate" to the list? According to Oxford, "degenerate" is a mathematical term "relating to or denoting an example of a particular type of equation, curve, or other entity that is equivalent to a simpler type, often occurring when a variable or parameter is set to zero."  —Preceding unsigned comment added by Gregherlihy (talk • contribs) 02:29, 30 August 2010 (UTC)
replies: text: Make it so 128.143.67.220 (talk) 20:48, 28 March 2011 (UTC)
thread_title:  Degenerate 

message: Although I understand what's meant by 'let', still, provided that I'm not native english, I wonder what does it actually stand for. Maybe it doesn't hold any extra information for a native speaker, I'm not sure. For me it does. For me it seems that something like 'let x be an integer' means something like 'let me speak about an integer variable and let me call/refer_to that particular integer variable as x'. But also it seems that it's not all about variables but is a very general notation instead.  — Preceding unsigned comment added by 80.99.93.173 (talk) 07:01, 31 January 2012 (UTC)
replies: text: My dictionary says that when used in the imperative, "let" is used to make a request or proposal. It's used this way in math more than usual, but the meaning is not specific to math so I wouldn't call it jargon. It's possible to rephrase it in different ways according to context, but rarely in a way that is as concise. To take your example, "let x be an integer" could be either "assume that x is an integer" or "choose an integer and call it x".--RDBury (talk) 17:54, 31 January 2012 (UTC)
thread_title:  Let 

message: I have added, based on experience in applied fields, that the word "tight" is often used with the same meaning as the word "sharp" in this excellent article. If someone with pure math experience can confirm that this is also the case in pure math (I am almost certain it is.. No field is an island, right?), please delete the "in applied fields" qualifier.  — Preceding unsigned comment added by 87.72.92.107 (talk) 21:07, 4 December 2013 (UTC)
thread_title:  Sharp = tight? 

message: I would very much like to see a clear definition/explanation for this phrase which is often thrown into the middle of a mathematical paper with little or no explanation. Keithbowden (talk) 12:45, 26 October 2014 (UTC)
thread_title:  (Not) enough open sets 

message: also sometimes used implying not only f(x) = 0, but also x\notin \mathrm{supp}(f)? I'm not sure, but by, you know, intuition... of course this wouldn't apply to infinity, though.--131.159.0.47 (talk) 14:11, 18 May 2015 (UTC)
thread_title:  Isn't "vanish at x" 

message: In Proof Techniques, index battle, in the phrase "for proofs involving object with plurious indices", what does "plurious" mean? It's not in Wiktionary, and there don't seem to be any relevant Google hits. - Adavies42 (talk) 13:51, 29 May 2015 (UTC)
replies: text: Hep, that wasn't English? If I remember correctly, the phrase was by me, and I'm no native speaker. In any case, it means or was assumed by me to mean "more than one" (multiple?), i. e., if you are familiar with Latex notation, expressions of the sort "x_{i_{j_{1}}}, x_{i_{j_{2}}}, ... , x_{i_{j_{n}}}".--131.159.0.47 (talk) 20:52, 5 August 2015 (UTC)
replies: text: Have replaced "object with plurious indices" by "objects with multiple indices", since, although I got the intended meaning, I doubt that the word "plurious" is currently English, if indeed it ever was; and we need either plural "objects" or singular "an object".  (Did Proto-Germanic even have an article?!) yoyo (talk) 16:14, 2 July 2018 (UTC)
thread_title:  "plurious"? 

message: These entries are amusing, but are they actually in use? I'd say cite or remove.  — Preceding unsigned comment added by 86.189.137.60 (talk) 03:28, 29 May 2016 (UTC)
thread_title:  Owl and Washing Machine 

message: Mathematicians often identify isomorphic structures implicitly, so they talk about "the field with two elements" or "the product of A and B" when really, any one of a variety of isomorphic (not identical) things will do. Arguably, this is not how we use "the" in everyday speech (one says "get some eggs from the store", not "get the eggs from the store). There is a whole page on nLab on this concept. Is it worth a mention? siddharthist (talk) 05:47, 31 October 2017 (UTC)
replies: text: Inasmuch as jargon is not just strange words, but also strange ways of using (or abusing) common words, the way we use "the" to denote a category of isomorphic objects certainly falls in the scope of this article.  And we who use jargon are often unaware we do so, so it would be good to inform non-mathematicians that "the" has this special meaning in maths.  yoyo (talk) 16:22, 2 July 2018 (UTC)
thread_title:  "The" 

message: In the article section Tetration#Non-elementary recursiveness, I noticed the abbreviation s.t., and wondered 
#whether readers with only basic mathematics experience in school would understand it;
#whether I should replace it with the phrase "such that"; and
#whether an explanation of such abbreviations belongs somewhere on Wikipedia.
The last point is what brought me to this page today.  Thoughts, please?  yoyo (talk) 16:30, 2 July 2018 (UTC)
thread_title:  Abbreviations 

message: Could someone contribute by offering a description of what is meant by 'essentially sharp'  — Preceding unsigned comment added by 92.20.85.81 (talk) 08:51, 5 November 2018 (UTC)
thread_title:  'Sharp' and 'essentially sharp' Could someone contribute by offering a description of what is meant by 'essentially sharp'  

message: Contrary to the following statement in  at by way of contradiction (BWOC):
Also, starting a proof or a sub-proof with Assume... indicates that a proof by contradiction will be employed
a proof starting with "Assume …" may continue with, e.g., "… without loss of generality …", or some other conventional phrase, without necessarily implying that the proof will assume a contradiction.  Therefore, I propose to remove this sentence entirely, after a suitable pause (a few days) for protest - or (and preferably) for convincing evidence to the contrary.  yoyo (talk) 17:45, 17 December 2018 (UTC)
thread_title:  Dubious 

message: Could someone please add an entry here for "admits", in usages like "X admits a Y-structure"? -- 86.147.207.61 (talk) 08:40, 21 June 2020 (UTC)
replies: text: Seconded. Can anyone find a WP:RS for an accurate definition of the usage of "admits"? Searching just finds things like Reddit and Stack Exchange (for example, this). -- The Anome (talk) 10:03, 20 August 2020 (UTC)
thread_title:  "Admits" 

message: I believe mathematicians sometimes use the phrase "kill" as an alternative to "mod out". Perhaps this should be mentioned in the article? There is also the method of "killing homotopy groups" in algebraic topology, which might be related (I don't know though because I haven't gotten that far in algebraic topology). Joel Brennan (talk) 23:40, 7 February 2021 (UTC)
thread_title:  "Kill"