Wikipedia:Articles for deletion/Normal set

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was DELETE. David Eppstein 00:14, 11 June 2007 (UTC)

[edit] Normal set

Normal set (edit|talk|history|links|watch|logs) – (View log)

Expired prod, de-prodded by Kurykh with edit summary de-prod, might be worthwhile, except might need references. The problem is that I don't think this is standard terminology at all. If references exist, we can discuss them (it's still possible, even likely, that the terminology is a nonce term for one or two references, in which case I would still favor deletion). --Trovatore 03:49, 5 June 2007 (UTC)

• Merge to set; by no means delete. This is interesting and a plausible search item. I learnt about this in high school. Resurgent insurgent 04:17, 5 June 2007 (UTC)
  • Can you find a ref, then? I have never heard this terminology, and I am a set theorist. --Trovatore 04:25, 5 June 2007 (UTC)
    • Found: "A normal set is a set which does not contain itself." - from a maths thesaurus published by Cambridge. Resurgent insurgent 04:35, 5 June 2007 (UTC)
  • There are several references on Google in the first 40 hits or so: I just checked. I don't have any old math books handy to check there, though. Merge per insurgent above. —Preceding unsigned comment added by SarekOfVulcan (talk • contribs)
• Comment I had tried Google previously and found nothing relevant. It's true that I didn't try adding "russell's paradox" to the search. Are all the references in that context? If so, I'd say merge to Russell's paradox, not to set. --Trovatore 05:02, 5 June 2007 (UTC)
• Delete. This is ad hoc terminology used in some presentations of Russell's paradox, not in use as a common meaning of "normal set" outside that context. Any exposition using it in the sense as defined here should contain its own local definition, and we should not sanction the elevation of ad hoc context-bound terminology to encyclopedic status by adding it to the Set article. It is unlikely that someone searching for some reason for "normal set" is served by a redirect to Russell's paradox. Some googling around found several, totally unrelated, uses, such as: the image of a normal space under a closed continuous map, or: a sample from a normal distribution.  --Lambiam^Talk 06:29, 5 June 2007 (UTC)
  • Comment - This definition would imply that the set of all normal sets is the Russell set (the set of all sets which are not element of themselves [1]), which redirects to Russell's Paradox. I don't like the idea of redirecting it there, however, as I'm sure there are other sets with this name. Perhaps a dab would be smart? Smmurphy^(Talk) 20:29, 5 June 2007 (UTC)
• Delete as an ad hoc term, per Lambiam. JPD (talk) 09:43, 5 June 2007 (UTC)
• Delete, per Lambiam. (And I've used "normal set" in various topological contexts, although I don't claim those usages are standard, either.) — Arthur Rubin | (talk) 20:20, 5 June 2007 (UTC)
• Delete. There is no common or generally accepted definition of this term within mathematics. For instance, I've just been working on Padé table, and in that context "normal set" can be taken to mean the portion of the table that is "normal" (and "normal" doesn't even mean "orthogonal" in this situation). DavidCBryant 11:23, 6 June 2007 (UTC)

It seems to me that it might be a useful search term. Do you think that making it a disambiguation page of sorts with links to different fields which use the term, and a quick paragraph on how it is used in each field? Smmurphy^(Talk) 13:51, 6 June 2007 (UTC)

I don't think it would be a good idea, just like it would not be a good idea to have a disambiguation page for, say, the terms "Normal method" or "Acceptable solution".  --Lambiam^Talk 16:06, 6 June 2007 (UTC)

• Delete. I tried to imagine what a plausible dab page might say: "In mathematics, normal set is an ad hoc term used by some authors to refer to several unrelated things..." Not a good idea... Geometry guy 19:50, 6 June 2007 (UTC)
• Delete. Not standard mathematical terminology. There are such things as normal spaces, normal subgroups, normal extensions, normal rings, etc, but sorry, I never heard of a "normal set"... — Turgidson 01:30, 7 June 2007 (UTC)
• Keep/Redirect/Merge. This is thoroughly standard terminology, although perhaps archaic, and encountered only in the historical context of Frege and naive set theory. Anyway, we already have a rather large article on this topic, its called Russell's paradox. I don't understand ZF very well, but I thought that one of the problems was that of counting to infinity (the axiom of infinity) and that the concept of a normal set somehow spun out from that. Whatever. I just read the commentary above, I see this point has been hashed out already. Anyway, a redirect to Russell's paradox is probably sufficient. Personally, I would have just speedy-redirected the whole thing, and not bothered with a prod/afd. linas 02:18, 7 June 2007 (UTC)

Comment. "Thoroughly standard terminology"? I beg to differ. I just checked MathSciNet, and there are 30 articles having "normal set" in the title (and 143 altogether with the exact phrase in the review text), but the meaning differs wildly -- which I think is normal for such an over-used term as "normal". Eg:

A subset $B\subset{\Bbb N}$ is said to be normal if the associated binary sequence defined by $i=1$ for $i\in B$ and $i=0$ for $i\notin B$ is normal, meaning that any binary word $\omega$ of length $|\omega|$ occurs in this sequence with frequency $2^{-|\omega|}$. MR2187788

A closed bounded set $S$ in $\bold R \sp n \sb +$ is said to be normal if $(S-\bold R\sp n\sb +)\cap \bold R\sp n\sb + =S$. MR2040059

A subset of $\bold R^I_+$, $I$ being a finite set of indices, is called normal if $g\in G$, $0\leq x\leq g\Rightarrow x\in G$. MR1769890

A set $M$ of real numbers is said to be normal if there exists a sequence $\Lambda=(\lambda_k)$ of real numbers such that $\Lambda x=(\lambda_kx)$ is uniformly distributed $\text{mod}\,1$ if and only if $x$ is in $M$. MR0308073

I could go on, but you get the idea. At any rate, why is the definition of "normal set" in this article any more standard than the others? Turgidson 02:36, 7 June 2007 (UTC)

• Delete: If normal set redirects anywhere, it should probably redirect to normal space, which is what I expected this article to be. Septentrionalis PMAnderson 20:04, 7 June 2007 (UTC)
• Disambig it seems like a widely used term with a variety of meanings, a disambig page with pointers to Normal (mathematics) and Russell's paradox seems the most appropate. --Salix alba (talk) 20:09, 8 June 2007 (UTC)
• Comment' I think a disambiguation page might be a good idea. It should not include purely nonce terms, but if the Russell-paradox meaning is one that many people have encountered, then there probably ought to be some reference to it, without the implication that it's what "normal set" can be understood to mean without further explanation. --Trovatore 23:31, 8 June 2007 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.