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Jon Awbrey 03:25, 3 February 2006 (UTC)
In the Relation algebra community this operation is invariably called converse. What's an example of a community that more commonly refers to it as inverse? -- Vaughan Pratt ( talk) 19:31, 18 January 2010 (UTC)
in general; in the case of equality it is in fact true that and are functions which are mutually inverse. Is this worth mentioning?
-- Daviddwd ( talk) 19:41, 14 September 2014 (UTC)
Perhaps then we really should call this the 'opposite relation' because that is what is naively expected, and also because the dagger functor on the category of relations assigning to each relation the opposite relation (in the opposite category) assigns with what is called here the 'inverse relation'. — Preceding unsigned comment added by Daviddwd ( talk • contribs) 20:37, 14 September 2014 (UTC)
I have a PhD in Computer Science, and I've certainly had reasonable exposure to math and logic over the years, but I find this article unbearably difficult to unpack. The main problem is the high density of jargon and the domain-specific notation. Obviously the reason for that is precision, which is important also. But the problem is that a definition of an unfamiliar term is often given in terms of 2-3 other unfamiliar terms, which in turn are defined in terms of more unfamiliar terms, etc.. I find myself diving through several layers of dependency definitions -- each with a different wikipedia page -- just to unpack one definition. And the problem with specialized notation is that it is not even clear how to look up the definition of a symbol such as "*" or (which I do know, but I'm just using as an example). Ask yourself: What would a reader type into a google search, to find out what the symbol means?
Examples help a lot. And plain language definitions help enormously, even if they are imprecise, though of course they should be clearly noted as being imprecise. The key point in a plain language definition is to avoid domain-specific jargon. For example: "Roughly speaking, a foo is . . . ". And later: "More precisely, a foo is . . . " (with full rigor and jargon).
As a case in point, I was just looking up the definition of "inverse relation" on wikipedia, and the explanation talked about a "semigroup with involution", so I had to look up that, which was defined in terms of a "semigroup", so I had to look up that page, which says that "A semigroup generalizes a monoid", so I had to look up "monoid" . . . except that I gave up at that point. :( (Stack overflow?)
There are two main use cases that a page like this should address, and they are different: (a) someone runs across an unfamiliar term and reads the page to get a rough idea of what that term means; and (b) someone wants to dig deeply and precisely into the meaning of the term. The (possibly imprecise) plain language definition should be given first, free of jargon. The gory details and jargon should come later. I do think it is important to introduce the jargon that is used in the field, but it should be fairly clearly separated from first providing a layman's (approximate) definition, so that readers can get the gist of what the term is about before they face the prospect of a deeply nested recursive traversal through many pages of jargon-filled definitions.
I hope the above suggestions are helpful and don't just sound like complaints. I know it is hard to write such things in widely understandable ways, and I very much appreciate the efforts of all editors who contribute. Thanks! -- DBooth ( talk) 16:38, 17 April 2015 (UTC)
In relation to the discussion above, on one hand it's probably important for the lead to warn/say that the inverse relation is not a group inverse and that it is an involution instead. On the other hand, it's not possible to cram all the necessary definitions in the lead to fully explain what this means. 86.127.138.67 ( talk) 05:50, 18 April 2015 (UTC)
As comments above indicate, Inverse relation is not appropriate as a title for this article which should be named Transpose relation or Converse relation. True, some early authors use Inverse relation, but propositions at heterogeneous relation show that, only under certain conditions, is the identity relation contained in the product of a relation and its transpose. Furthermore, on page 79 of Relations and Graphs by Schmidt and Strohlein, these comments precede an exercise:
Comments are invited; necessity for the Move seems apparent. — Rgdboer ( talk) 22:06, 18 June 2018 (UTC)
Move done. — Rgdboer ( talk) 22:28, 19 June 2018 (UTC)
And why is it a "poor idea"? — Rgdboer ( talk) 22:50, 21 June 2018 (UTC)
No reply! (Note the 2010 contribution above by Vaughn Pratt calling for Converse relation.)
Moving on: Completing a Move involves using "What links here?" to clarify article name-change. The redirect inversely related was found pointing here. No wonder the article was considered part of Project Statistics (negative correlation expresses inverse random relations) until June 19! Currently 48 editors Watch this article, but only 8 have reviewed recent changes. — Rgdboer ( talk) 22:19, 25 June 2018 (UTC)
I recently modified § Inverses, in part, to read:
Relations that are both right- and left-invertible are called invertible.
However, I had failed to notice that this was a direct quote from a reference, where the corresponding passage read:
Right- and left-invertible relations are called invertible.
User:Rgdboer, quite rightly, reverted my mistaken edit, for which I've thanked them.
However, a problem remains, to wit: the quoted text is ambiguous, and could easily be miscontrued to mean:
"a right-invertible relation is called invertible, and a left-invertible relation is called invertible".
I believe that the way I expressed the definition above is both correct and unambiguous – but I don't have a better source to hand than the ambiguous one presently in use. When time permits, I'll seek one to use here. yoyo ( talk) 05:01, 3 August 2018 (UTC)
The relation of set membership is instructive as an illustration of converse. Writing indicates a relation true when x is in the set A. If A is the range of the relation then the statement is always true, so presumably for a larger universe U. Thus the range of the set membership relation is the power set of U, written P(U). Set membership is then a subset of U x P(U). Its converse flips these factors.
This observation was put in the article 19 November 2018 and reverted 2 April 2022 . Discussion is invited. Rgdboer ( talk) 04:00, 2 April 2022 (UTC) Rgdboer ( talk) 04:07, 2 April 2022 (UTC) Rgdboer ( talk) 04:09, 2 April 2022 (UTC)
Okay. The thought provoking aspect of membership converse may be better discussed in Universe (mathematics) or in the Set membership article itself. The homogeneous relations < and > don’t bring up the non-commutative aspect of converse on domain/range that makes Set membership different. Rgdboer ( talk) 00:01, 3 April 2022 (UTC)
See Element (mathematics)#Formal relation for presentation elsewhere. Rgdboer ( talk) 01:22, 3 April 2022 (UTC)
Article now shows Rgdboer ( talk) 04:23, 6 April 2022 (UTC)
@
Rgdboer: @
Jochen Burghardt: The renaming of the article from "inverse" to "converse" was hurried and unjustified. Besides being more logical and intuitive, according to Google the phrase "inverse of a relation" is at least 5 times more common than "converse of a relation. (And indeed, even though I have used the concept for many years, I never seen it named "converse", or "transpose". I suppose that the "common" name depends on which sub-area of mathematics one lives in. Maybe "converse" is more common among logicians, by influence of (or specifically for) the "" logical connective?)
While it may not be worth reversing the move, "inverse" should definitely be listed as a synonym on the head paragraph, at least at the same level as "converse".
Jorge Stolfi (
talk)
15:37, 18 November 2023 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Jon Awbrey 03:25, 3 February 2006 (UTC)
In the Relation algebra community this operation is invariably called converse. What's an example of a community that more commonly refers to it as inverse? -- Vaughan Pratt ( talk) 19:31, 18 January 2010 (UTC)
in general; in the case of equality it is in fact true that and are functions which are mutually inverse. Is this worth mentioning?
-- Daviddwd ( talk) 19:41, 14 September 2014 (UTC)
Perhaps then we really should call this the 'opposite relation' because that is what is naively expected, and also because the dagger functor on the category of relations assigning to each relation the opposite relation (in the opposite category) assigns with what is called here the 'inverse relation'. — Preceding unsigned comment added by Daviddwd ( talk • contribs) 20:37, 14 September 2014 (UTC)
I have a PhD in Computer Science, and I've certainly had reasonable exposure to math and logic over the years, but I find this article unbearably difficult to unpack. The main problem is the high density of jargon and the domain-specific notation. Obviously the reason for that is precision, which is important also. But the problem is that a definition of an unfamiliar term is often given in terms of 2-3 other unfamiliar terms, which in turn are defined in terms of more unfamiliar terms, etc.. I find myself diving through several layers of dependency definitions -- each with a different wikipedia page -- just to unpack one definition. And the problem with specialized notation is that it is not even clear how to look up the definition of a symbol such as "*" or (which I do know, but I'm just using as an example). Ask yourself: What would a reader type into a google search, to find out what the symbol means?
Examples help a lot. And plain language definitions help enormously, even if they are imprecise, though of course they should be clearly noted as being imprecise. The key point in a plain language definition is to avoid domain-specific jargon. For example: "Roughly speaking, a foo is . . . ". And later: "More precisely, a foo is . . . " (with full rigor and jargon).
As a case in point, I was just looking up the definition of "inverse relation" on wikipedia, and the explanation talked about a "semigroup with involution", so I had to look up that, which was defined in terms of a "semigroup", so I had to look up that page, which says that "A semigroup generalizes a monoid", so I had to look up "monoid" . . . except that I gave up at that point. :( (Stack overflow?)
There are two main use cases that a page like this should address, and they are different: (a) someone runs across an unfamiliar term and reads the page to get a rough idea of what that term means; and (b) someone wants to dig deeply and precisely into the meaning of the term. The (possibly imprecise) plain language definition should be given first, free of jargon. The gory details and jargon should come later. I do think it is important to introduce the jargon that is used in the field, but it should be fairly clearly separated from first providing a layman's (approximate) definition, so that readers can get the gist of what the term is about before they face the prospect of a deeply nested recursive traversal through many pages of jargon-filled definitions.
I hope the above suggestions are helpful and don't just sound like complaints. I know it is hard to write such things in widely understandable ways, and I very much appreciate the efforts of all editors who contribute. Thanks! -- DBooth ( talk) 16:38, 17 April 2015 (UTC)
In relation to the discussion above, on one hand it's probably important for the lead to warn/say that the inverse relation is not a group inverse and that it is an involution instead. On the other hand, it's not possible to cram all the necessary definitions in the lead to fully explain what this means. 86.127.138.67 ( talk) 05:50, 18 April 2015 (UTC)
As comments above indicate, Inverse relation is not appropriate as a title for this article which should be named Transpose relation or Converse relation. True, some early authors use Inverse relation, but propositions at heterogeneous relation show that, only under certain conditions, is the identity relation contained in the product of a relation and its transpose. Furthermore, on page 79 of Relations and Graphs by Schmidt and Strohlein, these comments precede an exercise:
Comments are invited; necessity for the Move seems apparent. — Rgdboer ( talk) 22:06, 18 June 2018 (UTC)
Move done. — Rgdboer ( talk) 22:28, 19 June 2018 (UTC)
And why is it a "poor idea"? — Rgdboer ( talk) 22:50, 21 June 2018 (UTC)
No reply! (Note the 2010 contribution above by Vaughn Pratt calling for Converse relation.)
Moving on: Completing a Move involves using "What links here?" to clarify article name-change. The redirect inversely related was found pointing here. No wonder the article was considered part of Project Statistics (negative correlation expresses inverse random relations) until June 19! Currently 48 editors Watch this article, but only 8 have reviewed recent changes. — Rgdboer ( talk) 22:19, 25 June 2018 (UTC)
I recently modified § Inverses, in part, to read:
Relations that are both right- and left-invertible are called invertible.
However, I had failed to notice that this was a direct quote from a reference, where the corresponding passage read:
Right- and left-invertible relations are called invertible.
User:Rgdboer, quite rightly, reverted my mistaken edit, for which I've thanked them.
However, a problem remains, to wit: the quoted text is ambiguous, and could easily be miscontrued to mean:
"a right-invertible relation is called invertible, and a left-invertible relation is called invertible".
I believe that the way I expressed the definition above is both correct and unambiguous – but I don't have a better source to hand than the ambiguous one presently in use. When time permits, I'll seek one to use here. yoyo ( talk) 05:01, 3 August 2018 (UTC)
The relation of set membership is instructive as an illustration of converse. Writing indicates a relation true when x is in the set A. If A is the range of the relation then the statement is always true, so presumably for a larger universe U. Thus the range of the set membership relation is the power set of U, written P(U). Set membership is then a subset of U x P(U). Its converse flips these factors.
This observation was put in the article 19 November 2018 and reverted 2 April 2022 . Discussion is invited. Rgdboer ( talk) 04:00, 2 April 2022 (UTC) Rgdboer ( talk) 04:07, 2 April 2022 (UTC) Rgdboer ( talk) 04:09, 2 April 2022 (UTC)
Okay. The thought provoking aspect of membership converse may be better discussed in Universe (mathematics) or in the Set membership article itself. The homogeneous relations < and > don’t bring up the non-commutative aspect of converse on domain/range that makes Set membership different. Rgdboer ( talk) 00:01, 3 April 2022 (UTC)
See Element (mathematics)#Formal relation for presentation elsewhere. Rgdboer ( talk) 01:22, 3 April 2022 (UTC)
Article now shows Rgdboer ( talk) 04:23, 6 April 2022 (UTC)
@
Rgdboer: @
Jochen Burghardt: The renaming of the article from "inverse" to "converse" was hurried and unjustified. Besides being more logical and intuitive, according to Google the phrase "inverse of a relation" is at least 5 times more common than "converse of a relation. (And indeed, even though I have used the concept for many years, I never seen it named "converse", or "transpose". I suppose that the "common" name depends on which sub-area of mathematics one lives in. Maybe "converse" is more common among logicians, by influence of (or specifically for) the "" logical connective?)
While it may not be worth reversing the move, "inverse" should definitely be listed as a synonym on the head paragraph, at least at the same level as "converse".
Jorge Stolfi (
talk)
15:37, 18 November 2023 (UTC)