Talk:Cartesian product

Mathematics Start‑class Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-priority on the project's priority scale.

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

Questions to be clarified

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)

random notes

I must say, the deck of cards example is excellent. It caused me to link to this page instead of the very abstract one on worlfram mathworld. please keep it. --User:Brendan642

I second that. In fact, I came here to make just that comment! -- uFu 15:44, 15 July 2005 (UTC)[reply]

I also agree, and have come to the discussion page explicitly for this reason. It seems that these kind of concrete examples are extremely useful in understanding abstract mathematical concepts, and perhaps Wikipedia could use more of them in general. -- User:61.9.204.168 17/7/06 10:00 am (EST), from another computer

The deck of cards is brilliant. Does anyone know where it came from? If it's from a book I need to buy that book. 71.206.49.151 20:33, 13 November 2006 (UTC)[reply]

delete calendar format?

Does anyone see any use in this: "The Cartesian product can be introduced by the familiar calendar format"? If not then I'll delete it. I think it confuses more than it helps. — Sebastian (talk) 00:28, July 13, 2005 (UTC)

I agree. Paul August ☎ 01:44, July 13, 2005 (UTC)

nice article, some sugestion

What abour the properties for cartesian product? commutative, asociative,..? I like the article.

Capitalisation

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)[reply]

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. dbtfz ^talk 18:51, 29 April 2006 (UTC)[reply]

Index in the projection map section

I already made a correction in the past and it was reverted back! It's not a matter of greater clarity. It's actually correct this way, and absolutely wrong the other! the $i$ index in the formula is generic and spans over all the sets in the collection, whereas the $i_{0}$ is a specific index belonging to the set $I$ of all indices, and relative to the particular projection we are performing. If you don't distinguish them, the whole thing is just wrong, that's it. Think about it. I'm pretty sure of what I'm saying. Work it out with a specific simple example to verify it, if you don't trust me.

—Preceding unsigned comment added by Roccorossi (talk • contribs)

Er, no, the definition is perfectly okay as it stands. It's okay to use definitions with nested scopes.

The main reason I reverted was that you also changed a perfectly good edit (a mere comma, but there's no reason it should go away), and that you missed at least one i. I'm also unhappy with the double subscript, because it has accessibility issues and doesn't produce the right HTML.

Can we use j instead, or $i'$ , or something?

RandomP 17:01, 5 June 2006 (UTC)[reply]

I'm sorry but I have to disagree with you again. It really does matter because they refer to two different things. The "i" is the running index, so to speak, whereas the "i0" refers to the specific "dimension" onto which the projection is being performed, so they truly are different and it does matter! I went to Planet Math to check this, and I apparently am right. But they intelligently decided to use i and j instead of i an i0, so this time I followed suit and did the same thing, although I switched them because it was easier to edit the article that way.

Go here:

http://planetmath.org/encyclopedia/GeneralizedCartesianProduct.html

Please let's discuss this more instead of reverting back and forth. The last thing I want to do is give the impression of being arrogant or something, but I really am SURE of this. Let's talk about it, ok?

Roccorossi, is correct, the former was bad notation, the current is much better.

a.k.a. cartprod

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)[reply]

About the example in the intro

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)[reply]

I merged the example into the intro text, hopefully that will be better. - Francis Tyers · 08:35, 14 May 2007 (UTC)[reply]

Empty set

What's the Cartesian product of the empty set with itself and with a non-empty set?

I figure it must be the empty set, but I don't know. Someone put it up.

For any E E X Ø = Ø X E = Ø ; in particular Ø X Ø = Ø

Proof : forall z of E X F there's a x there's a y such that z=(x,y) and x is element of E and y is element of F -> if there's a z element of E X F neither E or F is empty. CQFD Michel42 16:28, 20 July 2007 (UTC)[reply]

Cartesian "explosion"

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)[reply]