Talk:Set-builder notation

I'm no expert, but I'm pretty sure that it doesn't have to be a monadic predicate, since they use the example p/q. --67.161.220.195 15:34, 10 August 2006 (UTC) what is the first recorded use of set bilder notation how about the first use of the phrase set builder notation

Add notation please

$\{a:\exists \ p,q\in \mathbb {Z} ,q\neq 0:a=p/q\}$

and

$\{k:n\in \mathbb {N} \land k=2n\}$

really don't mean a thing to me. What is the carat looking thing, for example? From messing around with the math tags I've gathered it means "and" but still, more about the actual notation would be nice. Jongpil Yun 07:01, 30 March 2007 (UTC)

OK, I added a little line about it. I think most mathematicians know what $\land$ means though, and otherwise they can easily look it up viewing the source or the alt text of the math images, to see that the TeX command (at least on Wikipedia) for it is \and. I must admit though, I never use it myself, I usually write a comma between conditions and when it's very formal I tend to just write out the words 'and', 'or', etc. —The preceding unsigned comment was added by CompuChip (talk • contribs) 18:25, 30 March 2007 (UTC).

Now what the hell is the backward E symbol supposed to mean? —Preceding unsigned comment added by 207.189.230.42 (talk) 22:09, 4 September 2007 (UTC)
It is the existential quantifier[[1]]. It means 'there exists'. 24.77.205.233 21:11, 15 September 2007 (UTC)

What is the use of a statement like " I think most mathematicians know what $\land$ means " in Wikipedia? An encyclopedia is for people who want an introduction to the field, please make my quotation unnecessary.--Damorbel (talk) 08:30, 3 July 2008 (UTC)

symbol translation

The Set-builder notation entry seems like a good place to list the various set notation symbols and their English translations.

Agreed, I came here looking for something along the lines of Modern musical symbols but with the Set Notation symbols of course. J.A.Treloar 217.169.50.138 (talk) 17:36, 10 March 2008 (UTC)

Thirded. This article is useless as it is. 140.247.241.116 (talk) 15:10, 11 January 2009 (UTC)

Unexplained second colon

The second colon in this example is never explained:
$\{a:\exists \ p,q\in \mathbb {Z} ,q\neq 0:a=p/q\}$
--Lambyte 08:11, 15 August 2007 (UTC)

This entry has been changed [2].

• $\{a:\exists \ p,q\in \mathbb {Z} (q\not =0\land aq=p)\}$

Although I'm asking myself why it is not written like this: $\{a:\exists \ p,q\in \mathbb {Z} \land (q\not =0\land aq=p)\}$ (with an additional AND). Can anyone explain? --Abdull (talk) 10:07, 18 December 2007 (UTC)

These things are mostly convention. Different scientific fields write the equivalent expression in a multitude of different ways, much like I could have written this sentence differently. Or at least that's what the mathematicians I know tell me. Pugget (talk) 13:58, 7 January 2008 (UTC)

No, this is not just convention. The two things you have put down mean quite different things. $\exists p,q\in \mathbf {Z}$ is a condition that is clearly always true ($\mathbf {Z} \neq \emptyset$), and this leaves q and p undefined in the second part of the condition. The first notation (no and) clearly links the two, and is read as "the set of all a where there exist p and q in Z such that q is not 0 and aq = p". The thing you propose says "the set of all a such that there exist p and q in Z [wasted ink; always true] and also that q is not 0 [for some undefined q] and aq is p [some undefined p and q]". The wedge separates the two conditions into two independent sub-statements. The article is correct at the moment.— Kan8eDie (talk) 23:17, 11 January 2009 (UTC)

Could do better on the explanation

The description seems to be written for those who already understand! I had to link here but in my description List_comprehension#Overview I broke down the syntax of the set comprehension expression I was using and explained each part. It would be nice if their were more explanation here. --Paddy (talk) 07:18, 30 July 2008 (UTC)