Talk:Intersection (set theory)

message: Why are so many SQL implementations incomplete in so many aspects? Is there a reason for why INTERSECT ALL is not implemented in other versiond of SQL, such as performance, complexity or lack of demand that can be inserted into this article? Zaphraud 05:26, 30 May 2007 (UTC)
replies: text: No JumpDiscont (talk) 03:15, 25 January 2010 (UTC)
thread_title: Untitled

message: I have the same problem comprehending intersection.
To me it doesnt seem like a viable operation because once you put a "line"/marker in the middle of  a box etc, the 2 small rectangles hence formed are seperate set.
so for example if I had a set of "all people in the school"
and I wanted to make a set of all girls in the school I could use references to the people in the database, but then the "reference" itself is pointing to some memory cell etc, so I am actually making another set which contains refrences to a set of memory cells which have girls. Is that correct?
Likewise, if I have a set of all people who wear red ties to school, then I have another set whose elements are memory locations of the people who wear red ties to school.
Now if I want to find all the girls who wear red ties to school, then either I do search on the set of girls or the set of girls or the set of reds to find the matching.
The answer I get is a set of memory locations of the girls wearing red ties which I have to "store" in another memory location.
This set may contain elements of the set girl and the elements of the girl red, but however, this is a set seperate from the base set of girls and red ties.  I mean one could also say that set contains ref to memory cells from the original set, but each of these references is always stored in a seperate set of cells..so it is indeed a seperate set.
Hence intersection cannot be a single step operation ever. It is like saying A.B is a subset of B, whereas in any digital circuit, one can tell you that A.B and B will have 2 seperate outcomes (they need 2 seperate LEDs to be percieved)
You can say B and B.A are the 2 events, however one would still say B is different from B.A , just like the domain name a.com is different from b.a.com
Note even if b belongs to a.com, it is a seperate entity and cannot be called a.com, it is called b.a.com  —Preceding unsigned comment added by Alokdube (talk • contribs) 06:37, 30 June 2008 (UTC)
replies: text: No JumpDiscont (talk) 03:15, 25 January 2010 (UTC)
thread_title: ====================

message: The discussion in the article appears to be confusing a difficulty with finding the right way to specify n-ary intersection in formal logic with the usual understanding of the n-ary intersection operation.
The usual definition of arbitrary intersection of M (under ZF set theory) is the set containing all the common members of all the member sets of M.
* If M={}  there are no members of members, so ⋂M = {}.
* If M has a single member {x} then ⋂M = x.
* If M has two members {x,y}, then ⋂M = x ∩ y.
* If M has three members {x, y, z}, then ⋂M = x ∩ y ∩ z 
* and so on...
Specifying it in formal logic is a bit tricky. Suppose we say ⋂M := ∃S∀z(z ∈ S)∀y(y ∈ M)( ∀y( z ∈ y)).  If M is empty, then this simplifies to ∃S∀z(z ∈ S)∀y(y ∈ M)().  This means that there are no constraints at all on S, i.e. the result of n-ary intersection.  This is not what we want so we need a different way of saying it.
A better way is ⋂M := ∃S∀z∀y(y ∈ M)(z ∈ S ≡ ∃ y ∧ ∀y( z ∈ y)).
This forces S to be empty whenever M is empty since z being an element of S is equivalent to saying that M has at least one element.  This fits much better with the normative understanding of the intersection of M.  (see http://tedsider.org/teaching/st/st_notes.pdf ,p. 7)
77.126.146.103 (talk) 20:03, 4 December 2012 (UTC)
thread_title:  Nullary intersection section seems odd to me too 

message: The phrase "If the sets A and B are closed under complement..." is confusing.  I looked up closure, this phrase says (i) if the complement of A is within A and (ii) if the complement of B is within B.  I suspect that the writer meant that A and B are within universe U, and (i) the complement of A is within U and (ii) the complement of B is within U.  From a nontheoretician, this seems obvious; it's hard for me to picture a case in which A, B, and U are defined in such a way that complementing A or B yields members outside of U.131.136.242.1 (talk) 22:44, 23 January 2013 (UTC)
thread_title:  Confusion in Basic Definition section 

message: Hello! I believe the Intersection page may need to be merged with this one, and partially into intersection (Euclidean geometry). I wanted to see what people thought about that first. 
As it stands, I don't think a "general" intersection page is useful or necessary.
To my understanding, something is either a geometric intersection (so can go to intersection (Euclidean geometry)) or a set theory intersection (and can go to this page). I think Intersection should turn into a disambiguation page. Otherwise, what should intersection be? I don't know what reliable independent sources we could cite that give a broad explanation of both and more.
What do you think? Should we keep intersection? If so, what should we put there? Turn it into a disambiguation page? IllQuill (talk) 06:13, 16 January 2021 (UTC)
replies: text: Arguing to bring all the intersection pages to the same place reminds me of the recursion wars. - Astrophobe (talk) 06:52, 16 January 2021 (UTC)

text: I've commented at WT:MATH. XOR'easter (talk) 17:26, 16 January 2021 (UTC)

text: This sounds a good idea to me; and the existing Intersection (disambiguation) page already seems enough afterwards, so I'd suggest redirecting the current Intersection there afterwards. It may be worth mentioning here that there's a fair bit of discussion on WT:MATH in favour of merging in the opposite direction: from Intersection (set theory) and Intersection (Euclidean geometry) into a single page renamed Intersection (mathematics) (which currently redirects to Intersection). (I'm personally against this approach and have explained my reasoning more fully on the WT:MATH page.) NeilOnWiki (talk) 17:25, 19 January 2021 (UTC)
replies: text: Closing, given no consensus and stale discussion. Most of the discussion was at WT:MATH: Wikipedia talk:WikiProject Mathematics/Archive/2021/Jan#Delete "intersection" page?, which seems to have been archived with no consensus and many different options being floated. Klbrain (talk) 09:05, 15 August 2021 (UTC)
thread_title:  Merge from intersection page