Talk:Map (mathematics)

message: Some symbols in the article do not appear in the intended way as hooked or two-headed arrows. Bo Jacoby 11:07, 20 October 2005 (UTC)
thread_title:  Busted symbols 

message: Around 1/16/06  most meaningful content from this page was moved to function (mathematics), since 'map' and 'function' are largely synonymous.  The consolidation will help avoid duplication.
There are several redirects that point to map, that should now point to function, where the content they refer to now lives, e.g. bijective.  I've fixed some of these.
Anyone contemplateing adding content here, rather than under function, should consider the consequences: links, duplication with function, etc.  LarryLACa 03:00, 20 January 2006 (UTC)
thread_title:  Content consolidated under function 

message: Every map is a correspondence (mathematics).218.133.184.93 05:37, 5 November 2007 (UTC)
replies: text: So?  Why is this not obvious from what's already there.  — Arthur Rubin |  (talk) 08:22, 5 November 2007 (UTC)

text: And why does it not require a source for it to appear in the article?  — Arthur Rubin |  (talk) 08:23, 5 November 2007 (UTC)
thread_title: Basics

message: A function is something whose range is a one dimensional.
For example the object  f : \mathbb{R}^m \to \mathbb{R}^n where m,n \in \mathbb{N}, is called a function if n=1 and a map (or mapping) if n > 1. Dharma6662000 11:21, 1 December 2007 (UTC)
replies: text: I don't think I've ever seen that usage.  — Arthur Rubin |  (talk) 16:51, 1 December 2007 (UTC)
replies: text: Probably someone used it that way but it is not generally known.  There is great variety of usage. Zaslav (talk) 08:00, 26 February 2011 (UTC)
thread_title: Simply untrue

message: um, an introduction and an example(or two?) applicable to a real world situation may aid understanding here, i'm not particularly uneducated - but understanding this article, i am not. :)  —Preceding unsigned comment added by 80.42.179.40 (talk) 11:01, 21 February 2008 (UTC)
thread_title: umm, what ?, please can you explain

message: Formally a map takes an element from a set A and outputs an element of set B. A function although similar has the restriction that every element in set A corresponds to one element in set B. for example the function f(x)=x^2 takes in a value and outputs only one value, for 1 its 1 for 2 its 4 etc. A map ||(x,y)||=1 or alternatively x^2+y^2=1 can output multiple values for an input. For x=1/sqrt(2) for example it outputs 1/sqrt(2) and -1/sqrt(2). Something that cannot happen in a function.  —Preceding unsigned comment added by Pirhomaniac (talk • contribs) 17:01, 19 February 2010 (UTC)
replies: text: I believe this not to be standard notation.  Have you a reference?  — Arthur Rubin  (talk) 17:52, 19 February 2010 (UTC)
replies: text: I agreed with Pirhomania. Then I checked my book and found I was wrong.
I think the confusion here is that in order to do something like calculus on a map you need to impose other conditions, and so in some lecture courses they talk about functions to mean (those maps which will work) rather than any map. Also (in Warwick, UK anyway) you often have questions along the lines of 
A map is defined as follows... is this map well defined?
When in reality the question is asking "is this a map?" - however the fact that their is no suitable word for what the question is other than map, the brain slowly absorbs the term 'map' for any old thing and 'function' for the maps which really are maps.
As it happens any map is a subset of the Cartesian product AxB, but not every subset (or pairing) is a map. So really the questions from uni could have used the term pairing. I believe they didn't because that would require more knowledge about set theory than they wanted to worry about in the first term of first year, and because it doesn't help to visualise what's going on.
Anyway I hope that cleared up some confusion. It may be noteworthy to say that colloquially in some universities the term map describes any pairing (subset of cartesian product) when questioning whether or not the map is well defined (i.e. genuinely a map).
--92.14.234.142 (talk) 22:33, 14 February 2011 (UTC)

text: The word "function" has a pretty standard meaning throughout math.  The term "map" is much more variable and often does not mean a function; it may mean a special kind of function, it may mean "morphism" which is more general than a function.  I adjusted the article in view of this diversity of usage. Zaslav (talk) 07:59, 26 February 2011 (UTC)
thread_title: A function is a special case of a map

message: Hi. MathWorld has nice explanation here, but I'm not sure where it should be placed. --Adam majewski (talk) 16:15, 31 March 2010 (UTC)
thread_title:  references 

message: A mapping is simply a tool to 'connect' two abstract (i.e. mathematical) objects. Mappings are usually given by
:
\begin{align}
M : A &\to B  \\    
      a &\mapsto b.  
\end{align}
which expresses how members from two sets of objects interact with one another. 
Since functions are also maps—for instance, f(x) = x^2  can be given as the mapping
:
\begin{align}
f : \mathbb{R} &\to \mathbb{R} \\
   x                 &\mapsto x^2
\end{align}
—the term 'map' and 'function' are sometimes used interchangeably.
p.s.
To suggest "map" is a synonym for "function" is like saying "animal" is synonymous with "horse".  — Preceding unsigned comment added by 66.11.191.243 (talk) 03:23, 21 September 2012 (UTC)
thread_title:  Suggestions for improvement 

message: Map is a synonym for function, there is no need to blurry the idea and confuse the readers. How one defines function exactly is still left open for everyone.
The whole thing here to me seems like a setup to change every word usual in set theory into category theory, which built on the perception that a function should have a definite domain and range, hence "map". --14.198.220.253 (talk) 13:35, 7 October 2013 (UTC)
replies: text: Such that other don't get confused too. Map is used by some as a synonym of function, that is true. But this is due to uses in texts written by authors that either were not aware of the difference or didn't want to make explicit the distinction. The key difference between maps and functions, is that map is a function (set of ordered pairs with unique image condition) together with its co-domain. They are the arrows in categories in which morphisms are functions. An elementary book that I remember in which the author was careful enough to perpetuate the misunderstanding is Apostol's Mathematical Analysis. There must be many others. Cactus0192837465 (talk) 02:04, 31 January 2019 (UTC)
thread_title:  Suggestion on removal , redirect "map" to "function" 

message: This seems a wiktionary article: it talks about different concepts bound only by the word used to describe them. I think it would be better to create different stubs about each of those concept and link to them from the map (disambiguation) page. What do you think?--Malore (talk) 06:04, 30 September 2018 (UTC)
thread_title:  Wiktionary or Wikipedia article? 

message: I think that maybe an approach that can serve to make this article a clear separate entity from others, is to dedicate it to the use of map as a concept in mathematics, specially when it is not used as a synonym of function. 
* Clearly the first very thing that the article should say is that very widely map/mapping and functions are used as synonyms. This first sentence should have, and it should be easy to provide it with, many references. There would necessarily be a link there to the article about functions. That article is already quite extensive, and contains all (if something is missing it can always be added) the information that map would have when they are synonyms. 
* But then say, as a second sentence, that the rest of the article will be dedicated to the use of map when this is different from the notion of function. This would include, both the cases in which the different notion is a homonym, like that use in graph theory mentioned in the article, but also for what distinctions are made by authors that purposely define functions and map/mapping as different concepts. 
It seems to me that explicitly saying that this is the purpose of the article, and making it so, would serve to both organize and give stability to its content. Otherwise, people convinced that being a synonym of function is the only use would be constantly leaning the content in that direction, people that are used to other uses going in the other direction.
* Links from other articles pointing here, would read soon the second sentence and be able to decide if they want to use the link in the first sentence to jump to the general article about functions, or stay in this one to see the particular material that the second sentence is telling them that this article is about. 
Thoughts? 
Would the title require to reflect such intention of the article too? I don't know if there are rules in Wikipedia about that. Cactus0192837465 (talk) 01:56, 2 February 2019 (UTC)
replies: text: I think we need a tie-breaker. To reiterate my position, I still don't think how this "page" can be turned into a genuine Wikipedia article. There are "concepts of maps", obviously; but, no single "concept" of a map. In my view (and in fact also of the others; e.g., #Wiktionary or Wikipedia article?), these concepts of maps are already covered elsewhere; function (mathematics), morphism (category theory), homomorphism, etc. In short, in the practical sense, this page functions as a disambig page. I don't know how to change that, without duplicating existing articles. -- Taku (talk) 23:53, 2 February 2019 (UTC)
replies: text: I think it would make a perfectly good set index article. —David Eppstein (talk) 04:41, 3 February 2019 (UTC)
replies: text: Agree; either that or leave it as a broad-concept article. -- Michael Bednarek (talk) 05:13, 3 February 2019 (UTC)
thread_title:  Concept article