Talk:Cartesian product

message: I feel a link to the coproduct \coprod is needed. MFH 22:20, 9 Mar 2005 (UTC)
thread_title: Untitled

message: The opening definition of this article is surely incorrect (or at least incomplete): "Specifically, the Cartesian product of two sets X (for example the points on an x-axis) and Y (for example the points on a y-axis), denoted X × Y, is the set of all possible ordered pairs whose first component is a member of X and whose second component is a member of Y"
As that does not apply with the empty set
81.178.193.188 (talk) 21:26, 25 October 2010 (UTC)
replies: text: nothing is wrong with the empty set here, the definition is precisely correct Halflingr (talk) 21:53, 15 December 2010 (UTC)
thread_title:  Cartesian product of the empty set 

message: could u explain why the cartesian product of 2 sets is an inefficient operation to perform
:I think your question is not well posed. As it stands, the answer might be: Because the sets could be uncountable sets. MFH 22:11, 9 Mar 2005 (UTC)
thread_title:  Questions to be clarified 

message: I was under the impression that "cartesian product", like "abelian group", had lost its capital letter by now.  We're inconsistent about it in the article.  I suggest adopting the non-capitalised spelling, just because it's the one I'm more used to.
RandomP 18:47, 29 April 2006 (UTC)
replies: text: I agree, though I think there should be a brief note to the effect that both conventions are commonly used.  At any rate, it should definitely be consistent one way or another.  dbtfztalk 18:51, 29 April 2006 (UTC)
thread_title:  Capitalisation 

message: A quick Google confirms that the hypocoristic cartprod is quite widely used. I don't know if that's encyclopedic. William Avery 14:24, 27 July 2006 (UTC)
thread_title: a.k.a. cartprod

message: I came to this page wondering what a Cartesian product was. The first sentence, first paragraph and ensuing formulas confused me. I didn't need to calculate it, just get an idea of what it was. I asked a friend of mine, and he explained it in the example I gave. I understood the idea immediately. Now I suck at maths. I'll grant that, but Wikipedia is supposed to be for people who suck at maths, and those who are good at maths. 
The example was removed by a guy who said that it was the same example further down. When I looked I couldn't find it. This is probably because I don't understand maths language. I'd like to (humbly) request that the example I added be left in the introduction for those of us who aren't very good at maths and for who formulas make reading difficult. - Francis Tyers · 08:15, 14 May 2007 (UTC)
replies: text: I merged the example into the intro text, hopefully that will be better. - Francis Tyers · 08:35, 14 May 2007 (UTC)
thread_title: About the example in the intro

message: Is there a technical term for the notion that a Cartesian product of several "small" variables grows quickly to an intractable level?  70.251.148.89 (talk) 02:18, 2 January 2009 (UTC)
thread_title: Cartesian "explosion"

message: I'm not a set theorist or anything but lemme get one thing straight:
Functions are defined as ordered triplets (X,Y,G). Now G is the cartesian product of X and Y, which needs the concept of ordered pairs to be defined.
Order tuples on the other hand are sometimes defined as functions from the naturals to a set. Now I know they need to be functions when talking about arbitrary infinite index sets, but IS THIS DEFINITION NOT CIRCULAR?
So does it work like this: ordered pairs and ordered triples are defined in terms of sets, then we can go on and on about functions and higher than 3 ordered tuples?Standard Oil (talk) 07:30, 2 July 2009 (UTC)
replies: text: Yes, that is one way to handle it. — Carl (CBM · talk) 12:03, 2 July 2009 (UTC)
thread_title:  Functions/ordered tuples 

message: Could someone please help me to proove the following formula: cartesian product of unions isn't equal to union of cartesian product: (AUB)x(CUD)=/=(AxB)U(CxD). My question is allso, which is the subset of which. Thank you for your answers!  —Preceding unsigned comment added by 193.2.111.106 (talk) 12:47, 30 July 2009 (UTC)
thread_title:  Please help! 

message: Cartesian product seems to have circular definition with direct product at the moment (idem per idem).  —Preceding unsigned comment added by 79.191.144.99 (talk) 23:19, 23 August 2009 (UTC)
thread_title:  Problem? 

message: This may be a stupid question but I am new to this so please bare with me.
Is there an inverse to Cartesian products, like separating a set, for example the cards, back into ranks and suits?
I understand it is simpler for examples like the above and probably doesn't work as well with numbers and probably not at all with infinite sets but is there any sort of concept for this?  — Preceding unsigned comment added by 109.148.177.203 (talk) 20:43, 12 June 2012 (UTC)
thread_title:  Inverse? 

message: Since the product of 3 sets is considered further on, I suggest that it be illustrated in the same way that the 2d Cartesian product is illustrated, for the sets A= {x,y,z} B={1,2,3} and C={Q,R,S}. This 3d diagram could illustrate the 1st several members of AxBxC as (x,1,Q), (x,1,R), which would show visually that Ax(BxC)=(AxB)xC=AxBxC.  — Preceding unsigned comment added by Vlittlewolf (talk • contribs) 16:06, 23 February 2014 (UTC)
thread_title:  product of 3 sets 

message: It seems a bit duplicate to expose the cartesian square twice, first in the intro and, then, in the powers section. Furhtermore, intro admits the square to be a product of heterogenous sets, whereas the powers imply that the square is the product of set with itself. --Javalenok (talk) 15:21, 19 August 2014 (UTC)
thread_title:  Cartesian square definition is contradictory 

message: : (→‎Non-commutativity and non-associativity: I can't find any scholarly study of associative ordered pairs and set-theoretic associative Cartesian products (e.g. not in Scott/McCarty "Reconsidering Ordered Pairs"))
I couldn't find a source either. However, I vaguely remember that strings (of length n) are sometimes defined as (n-)tuples. In that context, someone might have identified string concatenation with string pairing for simplicity, thus considering the latter as associative. In this setting, the Cartesian product is associative, too, and therefore can then be used to implement the concatenation operator in regular expressions. - Jochen Burghardt (talk) 15:37, 22 October 2014 (UTC)
replies: text: There are definitely associative Cartesian products out there — that exact phrase occurs in the literature. Commutative too. But I think they are for things like finite graphs rather than (what the section containing this subsection is about) abstract set-theoretic products. —David Eppstein (talk) 16:18, 22 October 2014 (UTC)
thread_title:  Associative Cartesian product? 

message: In the first paragraph we read: "for sets A and B, the Cartesian product A × B is the set of ALL ordered pairs (a, b) where a ∈ A and b ∈ B". But in my understanding this sentence is confusing and in contradiction to non-commutativity and non-associativity. I propose removal of the "all" quantifier because it suggests that for A = {1,2}; B = {3,4} the cartesian product is A × B = {1,2} × {3,4} = {(1,3), (1,4), (2,3), (2,4), (3,1), (3,2), (4,1), (4,2)} - 86.5.220.129 (signature supplied from history)
:The definition in the first paragraph is ok. In your example, e.g. (3,1) is not an ordered pair (a,b) where a∈A and b∈B, so it is not in A×B. - Jochen Burghardt (talk) 13:52, 1 August 2015 (UTC)
thread_title:  Set of ALL ordered pairs 

message: "In which the firs telement".... Must be" in which the first element".  NimXaif6290 17:27, 15 March 2017 (UTC)
thread_title:  Mistake in description of page 

message: I feel like a sentence to how it's produced in LaTeX could help: \times in LaTeX produces \times. (something like this should probably go to even more articles about maths) 2003:DF:F720:4E47:CA09:A8FF:FE26:39B4 (talk) 20:57, 24 June 2023 (UTC)
replies: text: That sort of content is generally in the articles about the symbols, rather than the articles about the concepts they symbolize. For this one, the article about the symbol is multiplication sign. It might make sense to include a link to that article somewhere early on in this one. —David Eppstein (talk) 21:21, 24 June 2023 (UTC)
thread_title:  How to write it in LaTeX