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question wikilinks something, I take it there may be some meaning I am not necessarily familiar with. "Well behaved" is vague at the best of times, but I would have expected that it would be well-defined when used in mathematics. That definition may be different in different use cases; fine. This article, if it should exist, should then state either this, or the different meanings. Now it attempts to do a little bit of both and ends up saying, in my eyes, nothing at all. The partial ordering at the bottom does not actually answer the question what "well-behaved" means, of course.
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554:(as the term is used in our article), it is not precise mathematical terminology. As such, its meaning is highly variable depending on context and speaker. A "well-behaved" object is simply one which has some property which, in the context we are talking about, we have decided is desirable. In some cases, it may be fairly clear-cut which properties are the desirable ones, in other cases less so, but the concept is not precise and there's always some room for argument. Thus in
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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
519:"better-behaved", which (along with the introduction to the list) begs the question where the 'line' for "well-behaved"ness lies. That may well be a nonsensical question from a mathematical point of view (I am still not quite sure!) but if there is no relation, the information should not be in this article. If there is, the relation should be explained better.
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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). --
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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
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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.
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It tries very hard to say something meaningful, and then fails. The partial ordering at the bottom (with which various people here disagree, clearly!) is not helpful either. It's like saying we want to minimize some number, but we're not going to tell you what domain that number is in (N, R, Z, some
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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
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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
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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
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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
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the first paragraph notes that the property of being measurable is the correct notion of desirability for functions between measurable spaces (this is one of the clear-cut cases; there's not really any other sensible notion of well-behavedness for such functions), the second paragraph gives the
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I see. So, I guess the main reason I am not satisfied by this article is that, although I speak a reasonable amount of
English, it is not my native language, and in mathematics "ordinary" words do not necessarily mean what they would mean in normal conversation. In particular, if the article in
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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
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article, all first three paragraphs seem to be three separate definitions for what "measurable function" means. It is not obvious to me what "well-behaved" as stated in the first paragraph means as related to the two other, distinct, definitions in the other paragraphs. Is its use in the first
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Perhaps that is what confused me about the article in its current state more than anything else: that it intends to accurately describe a topic, but then says on the one hand that there is no definition, and on the other that there are examples in which there is some agreed-upon meaning to
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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"
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about that requirement. What is it saying? Does the function need to be integrable? (how?) Does it need to be continuous? For all I know it needs to map from reals to reals and have a heart-shaped plot, and nothing else will do -- the page certainly gives no definition whatsoever.
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and editors are trying to explain the notion by giving examples of objects which are prettier (uglier) than other objects, and then ultimately saying that there is no absolute way to know, good luck. I am pretty sure that mathematical proof and requirements for functions are
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article to make it easier for weird people like me to understand the concepts more quickly, while maintaining accuracy. (Again, I would be bold, but I do not pretend to be a great mathematician, so I'd rather not make things worse than they are now) :-)
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precise definition of what a measurable function is, and the third paragraph gives an important special case. Whether it's a good idea for that article to start with a couple of vague intuitive sentences and then give the precise definition I don't know.
515:, I would be wrong. While there may be paradigm shifts, and these could be documented where and if necessary, it seems peculiar to just have an article that says that whatever the term means is up to the writer, but then still tries to say something.
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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
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paragraph actually identical to the adjective "measurable"? If not, how does the article define well-behavedness as necessary but not sufficient for measurable-ness? If so, why is using the term enlightening in this case?
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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. —
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The worst offense is the page saying "Of course, in these matters of taste one person's "well-behaved" vs. "pathological" dichotomy is usually some other person's division into "trivial" vs. "interesting"."
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I should apologise for ranting, I suppose - that was not my intention. I am glad you took the time to reply to my concerns, and hope we can figure out what, if anything, could be changed in this and/or the
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should not be (and that is what the article says at the moment!). The definition of eg. the reals does not change overnight, and while I would be perfectly entitled to hold a strong personal belief that
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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.
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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. --
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As I thought this article makes clear, 'well-behaved' is not a precisely defined term in mathematics. Despite your objections, mathematicians use a lot of non-precise
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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
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As for this being jargon, and use of it being a matter of taste - point taken. However, jargon still (by definition) has a definition. As you say, its
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I hope you don't mind my turning your response into the article. I'm not convinced yet that the article should be unlinked.
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subset, whatever), or how that domain is defined. We can tell you, though, that 3 is less than 5, and 6 less than 10.
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going to take out the aforementioned phrase right now, because it is so clearly utter rubbish that even I can tell.
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a mathematicians speaking of a "well-behaved function" means well-behaved in various other respects than that.
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I am not a mathematician proper, so I am not going to even try to fix this article, but someone better had. I
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What does well-behaved mean in mathematics? It is used all over
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Does it have something to do with how quickly a function changes, continuity, etc.?
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less, but the page definitely can serve the purpose of clarifying the term. --
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always seems to invoke continuity, and often also differentiability.
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A well-behaved function is one for which the Monte Carlo method works.
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a well-behaved region is one for which Newton's method works; in
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further or change it if you feel what I wrote isn't correct.
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A well-behaved region is one for which Newton's method works;
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that is what would be meant. Similarly, the meaning of
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a well-behaved function is one that is measurable; in
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may be subject to taste, fashion, etc.; however, its
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So, I came to this article trying to understand what
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