Talk:Correspondence (mathematics)

Old comment

So if you are doing a correspondence in R^2 how would you sketch G(x) = {y is an element of R^2 such that the dot product of x and y is 0} if G(3,4).

To which of the given definitions fits the character "≙"? --Abdull 21:05, 28 May 2006 (UTC)

This doesn't have anything to do with the article. Are you asking how to sketch a relation in general? If you mean ℝ², the sketch of G(3,4) on ℝ² is just the line y = -3/4 x. TricksterWolf (talk) 02:12, 7 November 2011 (UTC)

Compact-value

When people say a correspondence is compact valued, what do they mean? Jackzhp (talk) 16:22, 9 August 2010 (UTC)

Where do they say that? JRSpriggs (talk) 06:59, 10 August 2010 (UTC)

A bit late but a correspondence f:A->B is compact-valued if f(a) is a compact subset of the codomain B for every a in the domain A. — Preceding unsigned comment added by 83.100.157.125 (talk) 14:26, 27 December 2013 (UTC)

Economics

The following definition:

A correspondence "is a map f:A→P(B) from the elements of the set A to the power set of B"

is just a special function where the codomain consists of subsets of some set B, i.e. it is a subset of the Cartesian product AXP(B)

I am not sure that this is the most common definition of a correspondence in economics. I have seen the definition where a correspondence is defined as a relation R (a subset of AxB) that is "left-total" (i.e. for all a in A there is a b in B such that (a,b) is in R). There is an equivalence between the two definitions, but they are not identical because the former definition involves a subset of AxP(B) but the latter definition involves a subset of AXB.

The page on http://en.wikipedia.org/wiki/Multivalued_function does not even define a multivalued function formally. The page on hemicontinuity (http://en.wikipedia.org/wiki/Hemicontinuity) talks about correspondences using the second definition I gave above (although it does implicitly mention the connection between the two definitions under the secion "Other concepts of continuity" http://en.wikipedia.org/wiki/Hemicontinuity#Other_concepts_of_continuity). I think some work needs to be done to make these articles consistent and more complete. — Preceding unsigned comment added by 83.100.157.125 (talk) 14:24, 27 December 2013 (UTC)

References

There should be references or wikilinks for these definitions. Who knows some? Spaetzle (talk) 15:10, 16 August 2011 (UTC)

According to Relation (mathematics), a correspondence is a relation that is total for both the domain and target (i.e., a left-total surjective relation: the natural domain is the whole domain, and the image is the whole target). That differs from any of the definitions here. The Relation article cites "Klip, Knauer and Mikhalev: p. 3".

Related addendum: in computer science, correspondence is sometimes defined as a synonym for surjection (a left-total function that is onto but not necessarily one-one). In this context it refers to the manner in which data model the object they represent: all allowed concrete states must refer to a particular valid object, but multiple concrete states may represent the same object. This definition also differs from any listed here, but I could probably locate sources for this one if need be. TricksterWolf (talk) 00:57, 7 November 2011 (UTC)

Recent vandalism

This article is about the concept of correspondence, which is fundamentally different from the concept of relation. Check the references. Here are two screenshots for those who don't have access to them [1] [2] Cactus0192837465 (talk) 13:47, 5 February 2019 (UTC)

Of course, there is some variation (a subset vs a triple). But binary relation discusses both variations and the difference is not essential enough for separate articles (for example, Jacobson simply defines a correspondence as a binary relation; the difference is the writing style). —- Taku (talk) 17:08, 5 February 2019 (UTC)

Also, note “in algebraic geometry”, a correspondence is used as a subset; i.e., a binary relation in your language. —- Taku (talk) 18:33, 5 February 2019 (UTC)

Whether an article should be a redirect or not can be arrived at by consensus at WP:AfD. If multiple editors think that appropriate but one does not, that would be the correct venue for such a discsussion. Best wishes, Barkeep49 (talk) 21:51, 5 February 2019 (UTC)