Misplaced Pages

Revision as of 14:04, 4 May 2014

Template:Vital article

Mathematics C‑class High‑priority

This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Misplaced Pages. 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 C This article has been rated as C-class on Misplaced Pages's content assessment scale. High This article has been rated as High-priority on the project's priority scale.

Untitled

Older discussion (2002–) is at Talk:Naive set theory/Archive 1

Please Verify: (08/06/08)

"In symbols, A ⊆ B means that A is a subset of B, and B ⊇ A means that B is a superset of A."

This seems wrong to me, since the direction of the symbol and the elements are transposed in the second phrase. A⊆B is probably the same as B⊇A, but not the same as B⊆A or A⊇B.

Please Check!!! Thanks ~~user:lenehey

I think it is right now, but I think it is very confusing. Could we change to something like: "In symbols A ⊆ B means that A is a subset of B and B is a superset of A, whereas A ⊇ B means that A is a superset of B and B is a subset of A." (Still me.) Lenehey (talk) 19:01, 6 August 2008 (UTC)

Another Mistake?

In the 2nd paragraph of the section entitled 'Subsets' is the sentence:

Some authors use the symbols "⊂" and "⊃" for subsets, ...

The symbols "⊂" and "⊃" appear identical to me. Is this a mistake? —Preceding unsigned comment added by 115.166.28.14 (talk) 07:07, 19 April 2009 (UTC)

If those symbols appear identical to you, there's a mistake in your browser or your fontset. How *do* they appear? If they both look like a little box, or a question mark, or some nonspecific thing like that, it probably means you just don't have a font that can render them. --Trovatore (talk) 08:17, 19 April 2009 (UTC)

Yes, they looked like boxes. I was using Internet Explorer. I have viewed the page subsequently in Firefox and can see that they render differently (like different facing sideways letter 'U'). Sorry for the distraction! —Preceding unsigned comment added by 115.166.28.14 (talk) 05:53, 23 April 2009 (UTC)

Two meanings

I realized very recently, thanks to conversation with another editor, that there are two meanings of "naive set theory". The first is the meaning intended by Halmos in the title of his book: a consistent, informal analogue of axiomatic set theory. The second meaning refers to the "naive conception of set" as any collection of objects that satisfy a well-defined property; this is the sense people mean when they say "naive set theory is inconsistent". This article is certainly about the former meaning of the word. I'd like to be a little more clear about this in the "requirements" section, but for the moment I just added a note while I think about how that section could be phrased. One option would be for me to write an article Naive concept of set and then say here that this is not what is intended. — Carl (CBM · talk) 20:02, 19 April 2009 (UTC)

It's rather worse than that, and frankly I don't like the way content is assigned to article names at all. See the "Formalist POV" section in the stuff you archived, and my subsequent proposal (which I never got around to trying to implement -- I think you did a bit of it at some point, but matters are still not satisfactory).

The name "naive", for non-formalized set theory pursued at the research level, is bad because you don't expect active research to be "naive", even if we can then quibble about how some (by no means all) workers use the word in a non-pejorative sense.

Because of that, the division of content gives the impression that workers in set theory no longer accept that there is a clear intuitive notion of "set" to which the axioms must conform, and instead have adopted the axioms themselves as primary.

I have other objections to your formulation of "any collection of objects that satisfy a well-defined property", since according to the contemporary realist approach, the objects satisfying certain properties simply cannot be "collected" at all. That being the case, extensions of these properties do not enter into the "any collection of objects" part of the phrase, and so do not cause inconsistencies. What you really mean is more something like "given any well-defined property, the collection of objects that satisfy it", where the inconsistency can be traced to the existential import of the word the. --Trovatore (talk) 21:00, 19 April 2009 (UTC)

I want to temporarily ignore all philosophical issues to just look at the overall organization.

We did merge axiomatic set theory and set theory at some point. The basic stuff is in set (mathematics), which does seem to overlap a lot with the basic stuff here.

One option would be, then, to merge the elementary set theory from this article to set (mathematics) and then reduce this article to just discussing the various meanings of "naive set theory" and point the readers to the other articles for the actual material about sets. We could use Halmos' preface to explain what he means by "naive", and I have some other citations for the other sense. — Carl (CBM · talk) 22:19, 19 April 2009 (UTC)

I noticed in the archive someone pointed at fr:Théorie naïve des ensembles. The lede to that article does head in the direction I am proposing. But the google translation really butchers it. — Carl (CBM · talk) 02:32, 20 April 2009 (UTC)

I support the idea of making this article a discussion of the different meanings of Naive set theory, and leaving actual treatment of sets to set (mathematics). The duplicate content is unnecessary. Cliff (talk) 16:20, 4 May 2011 (UTC)

change operation into abstraction?

In section 1 paragraph 3 of the article, "As it turned out, assuming that one can perform any operation on sets without restriction leads to paradoxes such as Russell's paradox and Berry's paradox.", shouldn't the "perform any operation on sets" be "define sets by unrestricted abstraction"? voidnature 08:48, 19 June 2011 (UTC)

Article Motivation

Am I the only person who thinks the motivation for this article existing is a little weak. I mean couldn't we have a naive version of every mathematical area. It just seems dumb to me. 128.187.97.19 (talk) 18:13, 19 March 2012 (UTC)

The motivation for this article is that there's something called naive set theory (e.g. ISBN 0387900926) and we're describing it.--Prosfilaes (talk) 22:49, 19 March 2012 (UTC)

Gratuitous mention of "Boolean algebra (structure)"

In section "Unions, intersections, and relative complements", there is the sentence: "For any set A, the power set P(A) is a Boolean algebra under the operations of union and intersection."

Evidently this relates to the "Boolean algebra" structure, a relatively advanced topic. Readers of the current article are likely only to be familiar with boolean algebra (as in the Boolean algebra article), which is not the topic of this sentence, and will find this sentence confusing and in any case not useful. I suggest removal. Gwideman (talk) 00:24, 27 August 2012 (UTC)

Thompson

== Revising Naive set theory == Thompson (Neil Thompson 'Resolving Insolubilia: Internal Inconsistency and the Reform of Naïve Set Comprehension' Philosophy Study 2012 (2) ( 6) 417-431)) has suggested a means of revising Naive set theory that limits set comprehension by excluding set comprehension of sets isomorphic to Russell's set. Thompson claims that all paradoxes (save for Burali-Forti's and Goldstein's set schema which are excluded directly as contradictory descriptions) can be resolved in this fashion. The result is claimed to offer an ontology nearly as rich as that of Naive set theory.

This section keeps getting added to the article. I feel it's undue weight on one article and that it's misrepresenting this attempt to work around Russell's paradox as something fundamentally different from Zermelo–Fraenkel set theory or Quine's New Foundations, which it's not.--Prosfilaes (talk) 01:26, 1 May 2013 (UTC)

I also note that Philosophy Study is a journal found at http://www.davidpublishing.com/journals_info.asp?jId=680 , that the other articles posted in it are not mathematical articles, and that the publisher is not one of high repute; cf. http://chronicle.com/forums/index.php?topic=81342.0 . It's not a journal MIT gets, which brings up the question of whether anybody else does, and if anyone has seen it in the field to critique it.--Prosfilaes (talk) 01:49, 1 May 2013 (UTC)

First usage of ∈ – 1889 or 1888?

I just edited the article (see diff) and changed the date of the first usage of ∈ from 1888 to 1889 (found the later date here and in the book „Mengen – Relationen – Funktionen“ by Ingmar Lehmann and Wolfgang Schulz). The date 1888 was introduced with this edit 2003 by an IP. Is there any reference for the usage of ∈ before 1889? Greetings, Stephan Kulla (talk) 20:21, 21 April 2014 (UTC)

Although probably not a reliable source, Earliest Uses of Symbols of Set Theory and Logic agrees with you on the date. It also claims the earliest date for the symbol ∉ is 1939 by Bourbaki. --Mark viking (talk) 20:47, 21 April 2014 (UTC)

Definition of "naive theory"

To "In the sense of this article, a naive theory is a non-formalized theory, that is, a theory that uses a natural language to describe sets." I say, every theory uses a natural language to describe something. The formalization is done in a natural language, so there is always a natural language used. When in a formalized theory "The words and, or, if ... then, not, for some, for every" are "subject to rigorous definition", they are rigorously defined in a natural language. Cantors definition was a try to rigorously define the word "set"! 93.197.6.222 (talk) 20:44, 3 May 2014 (UTC) Thomas Limberg (Schmogrow)

Why did you call it "naive set theory" before I changed it, when you wrote "In naive set theory, a set is described as a well-defined collection of objects.". This is not naive! It's good work. It states "well-defined" so your paradoxes don't take effect. I have the feeling, you don't see the forest because of all the trees. After I changed it, it is a formalization of the term set. It rigorously defines it. The Zermelo-Fraenkel definition with all its axioms is not nesseccary. This definition here is better cause it generalizes the "set"-term. 79.252.242.192 (talk) 02:41, 4 May 2014 (UTC) Thomas Limberg (Schmogrow)

FYI, I have reverted all your edits. You are trying to insert your own thoughts (and to name them after yourself) into Misplaced Pages articles. This is original research, which is not allowed here. YohanN7 (talk) 13:42, 4 May 2014 (UTC)

But Misplaced Pages is so easy to use. Why is it forbidden to make research on it? And look, it's not like I've published a book with 300 pages here. My thoughts are very short. There are talk entrys which are much longer and you have probably read some of them. In my eyes it doesn't make a difference just because it's original research. 79.252.242.192 (talk) 13:51, 4 May 2014 (UTC) Thomas Limberg (Schmogrow)

It depends on what you mean. If Misplaced Pages is your subject of research, nobody will stop you. If you research in some topic that has a Misplaced Pages article, then you cannot use that article to promote your own research. The material in these articles should be verifiable. This means that they should have reliable sources. Reliable sources are usually third-party journals or books that cite the original research, itself presumably published in a reliable source. (And no, Misplaced Pages articles don't themselves qualify as "reliable sources".) YohanN7 (talk) 14:04, 4 May 2014 (UTC)

• C-Class mathematics articles
• High-priority mathematics articles