Talk:Complement (set theory)

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 Field: Foundations, logic, and set theory

There is also the symmetric complement or symmetric difference, see -- Nichtich 22:10, 12 October 2006 (UTC)

The second picture does not display correctly, or at least it did not display on my computer. Clicking on it, however, brought up the correct image.

Not actually defined[edit]

...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)

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)
Ah, that does make more sense now. Lead still needs work though, indeed. Thanks Paul! --Jubilee♫clipman 15:54, 27 December 2009 (UTC)
Ok, I've now rewritten the lead, I hope it is a bit better now. Paul August 16:02, 27 December 2009 (UTC)
Yes: that actually explains what it specifically is now! Good work. --Jubilee♫clipman 16:06, 27 December 2009 (UTC)

Proposition 2 given before Proposition 1![edit]

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)

Thanks for pointing this out. I've eliminated using the term "propositions" altogether. Paul August 14:35, 13 April 2011 (UTC)

A and B swapped in programming language examples?[edit]

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 (talk) 10:31, 2 November 2011 (UTC)

Or is it the other way around? Anyway, it seems like one or the other is wrong.. — Preceding unsigned comment added by Kayskull (talkcontribs) 13:40, 4 November 2011 (UTC)


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


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"? (talk) 23:11, 28 July 2012 (UTC)

Complements in various programming languages[edit]

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)

MINUS is not standard ANSI SQL, it's Oracle specific. Changed to EXCEPT