Talk:Interval (mathematics)

message: Let's say P1 = Q1 = 100 and P5 = Q5 = 500, but P2 = 197, P3 = 301 and P4 = 404, while Q2 = 200, Q3 = 300 and Q4 = 400——i.e., the "P" and "Q" endpoints are the same, while the "Q"s are equally spaced between each other, and the "P"s aren't.  For example (TN = "term number" and UT = upper TN):
:P_{tn}=F(x) G(y_{tn}) H(z)\,\!
while
:Q_{tn}=Q_1+\frac{TN-1}{UT-1}\Delta Q =P_1+\frac{TN-1}{UT-1}\Delta P\,\!
Would the proper definition/identification be "the Q's provide auxiliary points between P1 and P5 at a constant interval"?  Or does this concept have an established name?  This article doesn't appear to address this variation.  ~Kaimbridge~20:01, 16 February 2006 (UTC)
thread_title:  Varying vs. constant interval 

message: Let be I a set in functional space of all the functions f(x) defined on the interval  [0,1]  my question is if we can get some  I_1 , I_2,I_3,......  subsets of I, or if the case is more complicate dealing with numbers than with functions.--85.85.100.144 09:11, 19 February 2007 (UTC)
thread_title: Question for Functional spaces

message: Should it be noted that the Sun Studio compilers implement Interval Arithmetic?   --rchrd 03:13, 11 July 2006 (UTC)
replies: text: Done.--Patrick 09:39, 22 May 2007 (UTC)
thread_title:  Interval Arithmetic in Fortran and C++ 

message: It should be considered bad form to ask the user to reference another language edition of Wikipedia for more information, can anyone correct this? Anpheus (talk) 19:32, 20 February 2008 (UTC)
replies: text: Perhaps link to a google or babelfish translation.Tailsfan2 (talk) 16:19, 12 May 2008 (UTC)
thread_title:  Use of German Wikipedia Entry as a "See Also" 

message: I see several serious issues with the article, and I think it requires a comprehensive revision. Before going ahead and implementing this, I thought that I'd start a discussion. Following are problems with this article:
*Lede: The definition given excludes unbounded intervals such as [0,\infty).
*Also: interval is not a concept from Algebra. It has more to do with analysis, geometry and topology than with algebra.
*The section labeled informal definition basically talks about notation, not definition.
*The section labeled Formal definition speaks about intervals in ordered sets. When mathematicians speak of intervals, they usually mean intervals of real numbers. The mathematical definition of an interval is just a convex subset of the real numbers.
::Often, maybe. Usually, can't say. Always - absolutely NOT. SteveWoolf (talk) 05:38, 14 November 2008 (UTC)
replies: text: Seems like a good idea to me.  If I have time, I'll post with some more details.  But in the mean time, my suggestion is to be BOLD!  Cheers, silly rabbit (talk) 23:29, 15 April 2008 (UTC)
thread_title:  Rewrite required 

message: The concept of interval is both meaningful and useful for partially ordered sets in general.  This should top the article. Then give Real numbers as a special case.  As for the case of non-comparable elements a and b, the interval [a,b] will be ø, the empty set.
SLWoolf (talk) 16:25, 30 October 2008 (UTC)
replies: text: I agree to the extent that the general definition should be mentioned in the lede, not exclusively in a tiny section towards the end of the article. On the other hand, intervals of real numbers is what the vast majority of our users will expect here. And everything interesting that can be said about intervals in order theory really belongs into other articles anyway. Therefore in my opinion a single sentence at the end of the lede, pointing away to the appropriate article (partially ordered set) is enough. Not sure if I have the time right now; if I do, I will try to fix the lede and the little paragraph further down. --Hans Adler (talk) 19:09, 30 October 2008 (UTC)

text: OK, it's slightly more work than I thought because we need to change the definition (case by case for open, closed and half-open intervals). So I can't do it now. --Hans Adler (talk) 19:24, 30 October 2008 (UTC)
replies: text:  You don't have to change any definitions - but they could be much clearer. See the definition of Interval in Partially ordered set. In any case, your article is primarily about REAL intervals and should be renamed that. Not to do so is both incorrect and problematic for those of us who work with partial orders - we need to link to a general Interval definition. S0 - as you are busy, I have tidied things up for now - but technically this article should be renamed. An article specifically about gorillas, for example, should not be named "Great Apes". Hope you agree! Regards SteveWoolf (talk) 05:29, 14 November 2008 (UTC)
replies: text:  The title of the article doesn't have to be perfect, as long as it's easy for the reader to find the article they actually want. In this case, the note at the beginning that points to the article on posets should be enough to clarify the subject of this article. — Carl (CBM · talk) 14:54, 14 November 2008 (UTC)
replies: text:  As I said once, an article specifically about gorillas, for example, should not be named "Great Apes". It isn't correct to call an article Interval and then only talk about a subset of the subject. Of course, I realise renaming it is alot of work, since it has so many links to it. SteveWoolf (talk) 16:30, 14 November 2008 (UTC)
replies: text: On the other hand, as a mathematician, almost every time I say "interval" I mean "real interval"; this is probably true for everybody except order theorists. And readers who come to the article are most likely to be looking for the definition from their algebra or calculus class. So it's not quite the same situation here as with great apes, and I think that "isn't correct" is too strong a phrase for what's going on. As a somewhat parallel example, the article on concrete is about concrete bound with cement, even though asphalt concrete is also a type of concrete. — Carl (CBM · talk) 16:49, 14 November 2008 (UTC)
replies: text:  Okay, Maybe you're right. Be interesting if we actually knew what % of hits on the article were Real Intervals; but as you say, probably most. I'm happy with the article as it now is, so lets concrete it in and keep the apes out. (Just kidding) SteveWoolf (talk) 07:24, 17 November 2008 (UTC)
thread_title:  Why not define for ANY poset? 

message: To whoever anonymously wrote how he hates Calculus:
If you vandalise again, you will be reported. Why not try to make a postive  contribution to WP on a topic that interests you? Even sex, drugs and rock'n'roll are all valid topics. I also don't care much for calculus, but I expect you like using things whose production requires advanced mathematics, such as cars and planes and DVD's. SteveWoolf (talk) 12:08, 22 November 2008 (UTC)
thread_title:  Recent Vandalism 

message: In section Notation for intervals subsection Excluding the endpoints formatted math text:
: \begin{align}
(a,b) &= &]a,b[ &= \{x\in\R\,|\,a<x<b\}, \\{}
[a,b) &= &[a,b[ &=\{x\in\R\,|\,a\le x<b\}, \\
(a,b] &= &]a,b] &= \{x\in\R\,|\,a<x\le b\}, \\{}
[a,b] &  &      &= \{x\in\R\,|\,a\le x\le b\}.
\end{align} 
Does not agree with the last sentence of the subsection Excluding the endpoints
:Some authors use ]a,b[ to denote the complement of the interval ; namely, the set of all real numbers that are either less than or equal to , or greater than or equal to .
I don't know if the last sentence is to illustrate that not all authors follow the set builder notation prescribed by International standard ISO 31-11, or if it is an error an should be deleted to avoid confusion, since the meaning of ]a,b[ is already covered.— Preceding unsigned comment added by ‎8.30.81.10 (talk) 19:52, 28 December 2012
:I don’t see what set-builder notation has to do with the issue, but it’s clearly the former (i.e., a warning that some authors use the perverse bracket notation with a different meaning).—Emil J. 20:25, 28 December 2012 (UTC)
thread_title:  Error / Unclear Sentence in Notation for intervals section 

message: According to the article
:Alternate-bracket notations like [a .. b) or [a .. b[ are rarely used for integer intervals.
This statement is false (note that it has no citation), as in fields like computer science it is extremely common to note indices in this way. One such example is in the article one Zero-based_numbering which uses the integer range [0, n).
50.1.107.248 (talk) 01:01, 26 August 2014 (UTC)
thread_title:  Usage of open-ended integer intervals 

message: Both references to "[−∞, b] , [−∞, b) , [a, +∞] , and (a, +∞]" look like the change in notation doesn't match what the next is explaining; shouldn't it switch between open and closed for +/-∞ rather than a and b, since it's talking about the behavior towards +/-∞ ? Dirk Gently (talk) 13:10, 6 September 2014 (UTC)
replies: text: Consider what the article is saying more closely. These are all meaningless (and not to be used) in the context of the real numbers. However, in the extended real number line, the two infinities are actual elements (and not statements about limits), so including or excluding them makes sense. Bill Cherowitzo  (talk) 13:50, 6 September 2014 (UTC)
replies: text: The notations  ,  ,  , and  are ambiguous.  For authors who define intervals as subsets of the real numbers, those notations are either meaningless, or equivalent to the open variants. In the latter case, the interval comprising all real numbers is both open and closed,  =  =  =  .
Why would we make the statement that "equivalent to the open variants"? While some sloppiness in notation might occur, it surely makes no sense to document the closed variants on the real line as other than meaningless? And the claim of ambiguity also simply makes no sense? —Quondum 18:31, 6 September 2014 (UTC)

text: I agree, there is something a little fishy here. I find nothing ambiguous; if you are not talking about the extended real line, using the closed endpoint in these situations is just wrong. Also, in the real line case, those variants of  seem to be confounding the difference between closed interval and closed set and I suspect that no reliable source could be found for them. Bill Cherowitzo  (talk) 13:40, 7 September 2014 (UTC)
replies: text: I've updated the claims. I don't quite follow what you're saying about the real number case, though. —Quondum 20:13, 7 September 2014 (UTC)
thread_title:  Examples for infinite endpoints backwards? 

message: Compared to the substantive discussions above, this change, if it would be valid, would be just for consistency; but wouldn't it be better, so as to be more consistent with all of the other nearby examples in the section Classification of intervals, in the examples for left-bounded and right-unbounded, to reverse the positions of x and a, that is, to say a < x and a ≤ x ?  Wikifan2744 (talk) 00:34, 23 September 2014 (UTC)
thread_title:  A suggestion for consistency, helpful for non mathematicians   

message: I propose to merge the newly created stub values interval into this article (Interval (mathematics)). The content of that article appears to be talking about ordinary number intervals of the sort that this article already covers quite well, only couched in some of the language of signal processing. I'd love to get some input from someone knowledgeable about signal processing to clarify whether the phrase "values interval" is actually in common use in that (or any other) discipline, since it's not one I've ever heard before, and whether there's anything notably different about the way an interval of values is thought of, used, or described in that particular field to merit a separate article. In the absence of some clarification, I consider values interval a duplicate and would like to redirect it here.-Bryanrutherford0 (talk) 02:18, 24 September 2016 (UTC)
replies: text: I have to admit that I forgot what I wrote there (and it seems no longer accessible), but I remember that this was meant to help people from various background to understand better some aspect of the dynamic range, which is also in the end some relative of this very article for signal analysis folks. Probably some content from there might be useful in this article, to help clarify the relationship between dynamic range and values interval (range). Riccardo.metere (talk) 06:15, 24 September 2016 (UTC)

text: Probably, it should be somewhat referenced to Range (statistics) and Range (mathematics) as the concepts are sometimes overlapping but the term used around are always the same... Riccardo.metere (talk) 08:23, 24 September 2016 (UTC)
replies: text: It looks like it's been redirected by someone else.-Bryanrutherford0 (talk) 12:54, 24 September 2016 (UTC)
thread_title:  Merger proposal from Values interval 

message: Dyadic interval is defined in the text as [ k/2^n, (k+1)/2^n ] for some integers k, n. Maybe my brain isn't working today but as far as I can see such an interval is always of length 1 which makes little sense and contradicts what's stated in the paragraphs that follow after the def. Maybe someone could be kind enough to clarify. 84.219.174.71 (talk) 11:49, 13 January 2017 (UTC)
thread_title:  Dyadic interval clarification 

message: 5...7
5–7
5~7  — Preceding unsigned comment added by 2001:8A0:5E59:9F00:F092:4F6:C203:2042 (talk) 22:25, 7 December 2020 (UTC)
thread_title:  Could use a little section on international colloquial notation 

message: I am a student of class ten and I was doing math yesterday morning and a sudden I was faced of with a number that I named ultra irrational numbers, if I say you to give the root of 2 or 3 or 6 you wont be able, but can give an approximation but I will give you to write the root of a number but you wont be able to write a single line,; root -2, I know that no one can write a single line after this question,      I named it ultra irrational number because it looks like irrational numbers but these are unreal numbers, so I could be able to write 5 types of unreal numbers; infinity, -infinity, √-2,  infinitesimal, -infinitesimal MAKRI234 (talk) 11:03, 16 September 2022 (UTC)
replies: text: I suggest you read about Complex numbers. Dhrm77 (talk) 13:15, 16 September 2022 (UTC)
thread_title:  ultra irrational numbers 

message: Mathisfun is cool but this article needs more reliable sources .e.g books. AXONOV (talk) ⚑ 07:50, 29 March 2023 (UTC)
thread_title:  Mathisfun 

message: I prefer my version compared to yours.  seem to have made a positive comment about my version. In my opinion, it was a little hasty to restore your preferred version, because a consensus still forming. 慈居 (talk) 11:09, 17 September 2023 (UTC)
replies: text: What I said is that I think your later version was better than your earlier version that was the subject of the initial edit war, because it deferred the more technical topic to further down the page. I tend to agree with D.Lazard that the version with all of the explicit cases is a bit harder to make sense of as the primary definition of interval at the top of the page. I haven't ever thought about intervals in general posets so don't feel qualified to judge how that topic would best be presented. –jacobolus (t) 15:37, 17 September 2023 (UTC)
replies: text: The problem is that the primary definition doesn't work well in the poset setting. For example, any antichain will be an interval in that definition. We also have to consider the established term "convex set" and and all the derived terms such as "convex component", for the primary definition. The new definition is apprantly much longer, but it is an unambiguous definition. (An interval is a subset I such that I have one of the nine forms with respect to endpoints a,b\in\mathbb R\cup\{-\infty,\infty\}.) 慈居 (talk) 04:54, 18 September 2023 (UTC)
replies: text: I disagree for the same reasons I originally commented about. There's no reason why the principal definition this article gives for the real case needs to directly generalize to other (poset) cases. ByVarying | talk 12:40, 18 September 2023 (UTC)
replies: text: Why not? This is apprantly second to which is the actual standard definition, but the primary definition is not even a standard one, as seen e.g. in the reference below. And this is my personal experience, but at high school, I was only taught the endpoint definition. I wonder if this is the same for you, too. 慈居 (talk) 16:49, 18 September 2023 (UTC)
thread_title:  Current status of the consensus 

message: Following Jacobolus' suggestion, I'll take some time to further investigate and make a survey about the topics of intervals in posets and preordered sets. But before that, I have noticed a good (although I hate to say it) idea suggested by D.Lazard to write for posets and make a short note that it applies also to preordered sets. That's what I can accept, provided that It'll be clear from context that the formuation in the preorder setting is parallel to that for posets. And I can handle it. 慈居 (talk) 11:18, 17 September 2023 (UTC)
thread_title:  Intervals in posets and preorders