Talk:Complement (set theory)

message: There is also the symmetric complement or symmetric difference, see http://mathworld.wolfram.com/SymmetricDifference.html -- Nichtich 22:10, 12 October 2006 (UTC)
thread_title: Old and undated posts

message: ...a concept used in comparisons of sets to refer to the unique values of one set in relation to another
The above could applied to any set in relation to any other.  Is a complement not simply that which is not this?  Worse still, the term "relative complement" is used early on with out any other definition than ..."absolute" and "relative" complement refer to more specific applications of the concept.  These being?  --Jubilee♫clipman 00:15, 26 December 2009 (UTC)
replies: text: I agree that lead paragraph is not ideal. I will attempt a rewrite of this later. As for the use of the term "relative complement"  without definition, this probplem came about  by an editor switching the order of the sections "relative complement" and absolute complement" — I've now corrected this. I think the article should make more sense now. Thanks for pointing this out. Paul August ☎ 15:37, 27 December 2009 (UTC)
replies: text: Ah, that does make more sense now.  Lead still needs work though, indeed.  Thanks Paul!  --Jubilee♫clipman 15:54, 27 December 2009 (UTC)
replies: text: Ok, I've now rewritten the lead, I hope it is a bit better now. Paul August ☎ 16:02, 27 December 2009 (UTC)
replies: text: Yes: that actually explains what it specifically is now!  Good work.  --Jubilee♫clipman 16:06, 27 December 2009 (UTC)
thread_title: Not actually defined

message: This should obviously not be the case.  Either
* Rename the propositions, or
* Reverse the order of the sections "Relative complement" and "Absolute complement".
Jameshfisher (talk) 10:38, 13 April 2011 (UTC)
replies: text: Thanks for pointing this out. I've eliminated using the term "propositions" altogether. Paul August ☎ 14:35, 13 April 2011 (UTC)
thread_title: Proposition 2 given before Proposition 1!

message: Aren't A and B swapped in the programming language examples? The initial definition states that the relative complement of A with respect to B are the elements of B not present in A. However, the java example does a.removeAll(b), which leaves the elements of a not present in b.  — Preceding unsigned comment added by 212.62.245.98 (talk) 10:31, 2 November 2011 (UTC)
thread_title:  A and B swapped in programming language examples? 

message: This is often times denoted as Ā would be great to add to article. --ben_b (talk) 10:06, 30 April 2012 (UTC)
thread_title:  Ā 

message: I'm curious. Why is nonoccurrence called a "complement"? How does the lack of occurrence of an event make the description of the probability of an event occurring "perfect"? 68.37.254.48 (talk) 23:11, 28 July 2012 (UTC)
thread_title: Etymology

message: It's not clear that we need this long list of the names of operators in various languages: and it looks a lot like original research.  To justify it's inclusion, we should have a reference to an independent secondary reliable source listing languages with a "set" type and relative complement or set difference operators.  In particular, Unix shell does not have a set type, and using files as set types requires a lot more in the way of sourcing than a reference to a man page.  Deltahedron (talk) 19:47, 17 August 2014 (UTC)
replies: text: This list seems only tangentially related to the subject of the article, considering that the article is about the mathematical concept of a set complement. Everything in the list can also easily be found in the documentation of the languages, so I think it should be removed. If this really needs to exist, it should be moved to some other place, for example Comparison of programming languages. Clmul (talk) 22:02, 31 December 2017 (UTC)
thread_title:  Complements in various programming languages 

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thread_title:  External links modified 

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thread_title:  External links modified 

message: In my opinion of the two pictures the second does not contribute to the understanding of the term complement. One picture with red=A and white=its complement is more than sufficient. Madyno (talk) 08:43, 26 September 2018 (UTC)
replies: text: I disagree with that opinion which is why I reverted your change. For those of us who are comfortable with set notation and its visualizations, I would agree, one picture is sufficient, but for those readers coming to this page without that level of understanding, the two picture version is more informative. Another point to keep in mind is that all the Venn diagrams on this page have the subset being described in red, a uniformity that your edit destroyed. While this has nothing to do with the math, these subtle visual clues are often helpful to the novice. --Bill Cherowitzo  (talk) 18:55, 26 September 2018 (UTC)
thread_title:  Pictures 

message: I have removed the long list of the names of the function "set complement" in various languages. Several reasons for that:
* Not really encyclopedic
* Some of these languages do not have any builtin data structure modeling finite mathematical sets. So the list is confusing
* This is an article about mathematics, and this list is out of scope here. 
* This list breaks the guidelines of MOS:CODE and MOS:MATH#Algorithms. In particular, the lattes says 
However, it is worth to have in this article an explanation of the relationship between the mathematical operation of set complement and the programming operation of the same name. I have written such an explanation, which deserves probably to be expanded.
D.Lazard (talk) 12:29, 7 January 2019 (UTC)
thread_title:  Sets in programming languages 

message: We have that AND maps to INTERSECTION, and OR maps to UNION.
Does anyone have any references for the maps to RELATIVE COMPLEMENT (tt:0100) and also we have MATERIAL IMPLICATION maps to ABSOLUTE RELATIVE COMPLEMENT (tt:1011), and for the other logic operators?
Darcourse (talk) 04:00, 14 February 2021 (UTC)
replies: text: See Indicator function for the general relationship between subsets and functions with values in {0, 1}. For your case, you have to consider a bit string as a function that maps the position of a bit in a string to the value of the bit. The remainder is a simple computation for translating the definition of a logical operator in terms of AND, OR and NOT in term of operations on sets. D.Lazard (talk) 09:05, 14 February 2021 (UTC)
thread_title:  Maps to logic operators