Deimos 28

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context-setting

Hello. Please note that Wikipedia deals with a large number of subjects. One should not begin an article by saying "Let X be a parametrized family of probability spaces that ..." etc., before informing the reader that the article is about mathematics or statistics rather than poetry, 18th-century chemistry, theology, music, politics, chess, etc. E.g.,: "In statistics, a robust estimator is a ....". Also note that one should set the title word or title phrase in bold at its first appearance. Michael Hardy 21:19, 11 October 2005 (UTC)

Re: Setting the context

Hi there,

First of all, the capitals in the titles were put in on purpose: it is not uncommon practise and was required of me when I wrote my thesis. Anyway, I don't think it's a major issue and I don't really care either way. However, I will abide to putting words in bold at their first occurence and specify what the context is in future articles, as I consider it to be good advice.

Then, as far as introductory passages are concerned, I sometimes write them and sometimes not - it depends how much courage I have on a given day... Of course, I think there *should* be an introductory passage of some sort and I'm quite happy for other people (such as yourself for example) to write it if I haven't. I don't think the author of an article should be responsible for a complete coverage of the subject, nor for a perfect article: if you think something needs rewriting, feel free to do it. If I disagree, I'll tell you as I've put a watch on all the articles to which I have contributed.

In the former version of the estimator article, you didn't define what $\theta$ was (or ${\hat {\theta }}$ for that matter...): I consider that setting the context isn't merely to put a few hand-wavy explanations at the beginning of an article, but also to define precisely the mathematical beings you're using so that the reader knows what you're talking about (which is the only thing I like about maths actually).

Wow

You are really doing great over on Regression analysis. Thanks again. James S. 12:31, 13 January 2006 (UTC)

Thanks! As I more or less messed it up in the first place, I'm trying to do things cleanly now... At least, it showed me I really didn't have a clue what regression was about... ;)

Least-squares article

You're welcome, though I did little more than close the AfD according to consensus. Hopefully the AfD comments actually helped you improve the article, and no hard feelings came about :-) --Deathphoenix 22:51, 27 February 2006 (UTC)

Fourier Series

Hi, your edits at fourier series are of course welcome. But keep in mind that conventionally, these pages should be constructed from least complicated to most complicated concepts. Some of your edits make the content that was simple, into content that may conform to the norms of formal mathematical definition, but are much more difficult to interpret. Please keep in mind the audiance that will be viewing these pages. Fresheneesz 07:05, 12 March 2006 (UTC)

Replaced figures

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Characterizations of the exponential function

Hi, I noticed that you added a fifth characterization to the above article, the fact that the exponential function is the only continuous morphism from addition to multiplication. I've seen this proved in a couple of places (e.g. it is a homework problem in Rudin for the reals), but I haven't seen any proof (or even a claim) that continuity is a necessary condition.

Do you have a reference that shows that continuity is necessary, as I suspect it is? Thanks!

(The Wikipedia article is silent regarding whether continuity is necessary, so I'm not challenging the correctness of your edit. It just seems incomplete.)

—Steven G. Johnson 05:57, 13 February 2007 (UTC)

Suppose you've proved that the exponential function is the only continuous function satisfying

f(x + y) = f(x)f(y).        (*)

and

f(1) = e.        (**)

What do you mean by saying continuity is "necessary"---i.e. necesary for what? Necessary for it to be an isomorphism from the reals with addition to the positive reals with multiplication? It's not necessary for that, if you allow the axiom of choice. You can use the seemingly weaker hypothesis of monotonicity. That might superficially appear to mean you don't need continuity, but since it's enough to narrow it down to just one function, and since that function can be shown to be continuous, in that sense continuity is necessary. Now you could ask: How do you show that the unique monotonic function satisfying the identities (*) and (**) is in fact continuous? That could be what is meant by "How do you show continuity is necessary?" But that can't be what you meant since you were assuming continuity. Since Lebesgue measurability and the identities (*) and (**) are also sufficient to narrow it down to just one function. Generally, Lebesgue measurability is a weaker condition than continuity, so you could say in that sense continuity is not necessary, but on the other hand, Lebesgue measurability and the two identities (*) and (**) are enough to entail continuity (since the unique function satisfying those conditions can be shown to be continuous), so in that sense, continuity is necessary. Michael Hardy 13:02, 26 August 2007 (UTC)

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Proposed deletion of File:Periodic identity.jpg

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