Talk:Well-behaved

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What does well-behaved mean in mathematics? It is used all over Wikipedia, but not defined.

Does it have something to do with how quickly a function changes, continuity, etc.?

— Rlschuh 20:48, 2004-03-31.

It just means "behaves in a way which make it suitable for a certain field of study". It's the ordinary English meaning of "well-behaved". The nice behaviour is the one described in the original article. For example in Measurable function a well-behaved function is one that is measurable; in Newton's method a well-behaved region is one for which Newton's method works; in Monte Carlo method a well-behaved function is one for which the Monte Carlo method works. And so on. I suggest you remove the links you added, but leave this page for other readers who might imagine that there's a technical meaning. — Gdr 21:06, 2004-03-31.

I hope you don't mind my turning your response into the article. I'm not convinced yet that the article should be unlinked.

I have a vague impression from math, physics, and engineering classes I took that there is some more specific meaning. If the definition is just what you're describing, then many statements become circular if they use the description of something being well-behaved to explain why it works for that well-behaved thing. -rs2 21:37, 31 Mar 2004 (UTC)

What you did is fine but you should have edited it. Properly understood, none of the uses of "well-behaved" makes a circular definition. For example, in Measurable function "well-behaved" isn't part of the definition, it's an additional piece of information. And in Newton's method the method itself doesn't use the term "well-behaved" so it's not circular for a "well-behaved" region to be one where Newton's method works. There's no single technical meaning of "well-behaved": each field of study has its own typical meaning or maybe several typical meanings. For example, in functional analysis, there are several kinds of "well-behaved" function: continuous, monotonic, differentiable, infinitely differentiable, integrable, etc. — Gdr, 21:47, 2004-03-31.

Whoever wrote this somehow expects it to be understood that mathmematics rather than some other subject is what this is about, even though it does not say so. That is a profoundly absurd assumption. Michael Hardy 23:25, 31 Mar 2004 (UTC)

I had rather put this article in VfD. Good behaviour cannot be explained as a mathematical concept more than in real life (it is something that depends on context, culture, time, space and probably colour). Pfortuny 11:35, 2 Apr 2004 (UTC)

I'm almost convinced it should be unlinked from other pages, but it almost definitely has value as an entry. Unlike its common usage, "well-behaved" is often used as if both it had a clear meaning and the reader should know what that meaning is. I'm starting to suspect authors should use the term less, but the page definitely can serve the purpose of clarifying the term. --rs2 16:55, 2 Apr 2004 (UTC)

[edit] misleading examples

Someone inserted these lines before the initial informal list of examples:

• A well-behaved region is one for which Newton's method works;

• A well-behaved function is one for which the Monte Carlo method works.

Usually a mathematicians speaking of a "well-behaved function" means well-behaved in various other respects than that. Sometimes that is what would be meant. Similarly, the meaning of well-behaved region given above is just one of many; the meaning varies with the context, and the phrase is used when the context is expected to make clear which kind of good behavior is intended. It is highly misleading at best to say something that could give the impression that "well-behaved function" usually means one for which a Monte-Carlo method works. Michael Hardy 18:03, 19 Apr 2004 (UTC)

Sorry about my "misbehavior" here. I see that I was not being a well-behaved editor. Thanks for (a) catching, (b) fixing and (c) telling me about my mistake. I will be more careful in the future. --Uncle Ed 20:29, 19 Apr 2004 (UTC)

I actually do not like the "Euclidean space being considered more "well-behaved" than the non-euclidean space" example. I dont think that it is better behaved. This may just my knee-jerk reaction though to someone saying something uncommon is not as nice or well behaved rather. What nice property is there that we have for a euclidean space that does not work elsewhere? I may very well be completely wrong on this, but at least i will learn something. Also, I like the use of the term nice, there is this idea of allowing people to lie, and using 'nice' works for that very well, it expresses what you want: "not the pathological counterexample you are concocting" -sean, math student

i feel that the page is too simplistic. what's well-behaved and what's not? it is not clear at all to me why a riemann-integrable function is better-behaved than a lebesgue-integrable function. fair enough, lebesgue integrability is a weaker notion, and therefore it's (in some contexts) more natural. in particular, via lebesgue theory it's possible to prove more results than via riemann theory. so what? i think there's a difference between truly well-behaved vs. ill-behaved cases (say, a stable system vs. an unstable system) and weaker vs. stronger properties (say, a once differentiable function vs. a twice differentiable function). --Deliou 08:13, 27 September 2007 (UTC)

[edit] In physics

Physicists also throw around the term "well-behaved" a lot. Usually they mean it roughly as discussed (following whatever rules are needed for easy analysis,) with an additional implication of "something I won't have to consult a mathematician about."  :-) With respect to functions, it almost always seems to invoke continuity, and often also differentiability. Isomorphic 20:44, 19 Apr 2004 (UTC)

[edit] Separating

Reading the article again, it seemed to me that there are two slightly different definitions going on - one purely aesthetic, and the other practical. I put in the more practical definition that I'm used to hearing in physics, and separated it out from the aesthetic definition. Feel free to clarify further or change it if you feel what I wrote isn't correct. Isomorphic 21:14, 19 Apr 2004 (UTC)