Talk:E (mathematical constant)/Archive 1

message: The article says: 
:In 1975, the Swiss Felix A. Keller discovered the following formula that converges in e ("Keller's Expression" Steven Finch, mathsoft):
:: e = \lim_{n\to\infty} \quad {\rm }\frac{n^n}{(n-1)^{(n-1)}} - \frac{(n-1)^{(n-1)}}{(n-2)^{(n-2)}} \quad {\rm for}\quad\left|n\right|>2.
:This formula was published for the first time 1998 on Steven Finch's website www.mathsoft.com/asolve/constant/e/e.html.  He refers to it as “Keller's Expression”.</pre>
This is a delightful formula, but I have some problems with the way the description is written.  First, the referenced document is not available (404).   Second, it seems unlikely that the formula was first discovered in 1975.  Even if it was never published before (which I rather doubt) I think that's more likely to be because it is so simple to prove.  The formula looks mysterious at first glance, but really it turns out that the left term approaches n·e and the right term approaches  (n-1)·e; this can be proved in about two steps of simple algebra, directly from the definition of e.  Google search doesn't turn up anything relevant for "Felix A. Keller" or for "Keller's Expression".  So we have a formula here which could be discovered in ten minutes of idle tinkering by any bright undergraduate, but it's being credited to Mr. Keller as though it were a big discovery.   That seems strange to me.  Formulas usually only get names when they are important or at least surprising (Stirling's formula, Euler's identity) and this one is neither.  -- Dominus 14:38, 10 Mar 2004 (UTC)
replies: text: I've removed another insertion of "Keller's Expression" (together with proof) today.  Paul August ☎ 16:32, 23 January 2006 (UTC)
replies: text: I actually included a form of "Keller's expression" in the article, under the proviso that it is derived from simple algebraic manipulation of the basic limit def.  I think it should be in there for its intrinsic formal beauty.  Perhaps I should add a note about "keller's expression" beside the formula to prevent this type of thing?--Hypergeometric2F1[a,b,c,x] 06:53, 24 January 2006 (UTC)
replies: text: Perhaps, but it would need a reference. Where did you get that limit from? Did they call it "Keller's expression"? Paul August ☎ 14:35, 24 January 2006 (UTC)
replies: text: I got it from mathworld.  I dont recall a reference, but it is the same thing as Keller's expression, just made into a more pleasing form.--Hypergeometric2F1[a,b,c,x] 04:36, 25 January 2006 (UTC)
thread_title:  "Keller's Expression" 

message: 1. The text should say
:Alongside the number π and the imaginary unit i, e is one of the most important numbers in mathematics.
* Support Oleg Alexandrov (talk) 23:32, 15 November 2005 (UTC)
replies: text: Alongside the number π, e is one of the most important transcendental numbers in mathematics.
*Support Kdammers 07:05, 25 January 2006 (UTC)
thread_title: Poll

message: I don't think the definition of e^x should be in this article, that is why I took it out.  It could say that e is related to e^X or something but the topic of e^X is so huge that it should warrant its own article (which it has) and should not bleed in to this one about the NUMBER e.--Hypergeometric2F1[a,b,c,x] 04:47, 22 December 2005 (UTC)
replies: text: I disagree. The number e is not useful by itself, but rather, as the base of the exponential function. Cutting off e's most important application leaves this article without a good motivation. Oleg Alexandrov (talk) 05:08, 22 December 2005 (UTC)
replies: text: This is why I said that something like "e is related to e^x see corresponding article" or something like that could be put in there.  I think it is misguided to start of the "properties" section of the NUMBER E with a definition of the function e^x.  But then again, no laymen one is probably going to look at this anyway so whatever.--Hypergeometric2F1[a,b,c,x] 05:18, 22 December 2005 (UTC)

text: I agree with Oleg. The properties of e^x are properties of the number e. Since Hypergeometric seems to have acquiesced I'm going to restore that content. I think it is fine to start the properties section with it, but I'm open to consider other placement of this content. Paul August ☎ 06:07, 22 December 2005 (UTC)
replies: text: Hyper, you did a great job in adding new content, and I think we all appreciate your contributions, so thanks very much for that, and I'm sorry I didn't say so sooner. Wikipedia is a collaborative work, and that takes a bit of getting use to, and it is important to figure out how Wikipedia works, if we are all going to get along. For example, marking edits to article pages (no one cares about marking edits on talk pages) as minor or not, as appropriate, is a convenience and a courtesy to your fellow editors. It is a long-standing practice that other editors will expect and appreciate, and as you will see as you gain more experience, makes life a little easier for all of us. You will also have to expect people to edit what you write, (just like you edited what others wrote) and to make comments like the above. Sorry if you think some of us are "nitpicking" but unfortunately since I was born with the curse of a perfectionist personality, picking nits is one of the things I do, and since we are all volunteers, we have the luxury of dealing with either the trivial or the important as fits our inclinations. When you say you see a lot of us "sitting around doing nothing", well we are all free to do that as well, if we like. But If you look at any of the contribution lists — which you can do by going to a users page and clicking on "User contributions" — for any of the editors who commented above (or who contributed to the discussion on the Mathematics project talk page), I think you will find that they have all been doing rather a lot actually (notwithstanding the obligations of the real world ;-). Anyway thanks again for your contributions, I think they have made the article much better. Paul August ☎ 13:32, 22 December 2005 (UTC)

text: Merry Christmas Hypergeometric, and a Happy New Euler number (whether raised to x or not). Oleg Alexandrov (talk) 18:56, 23 December 2005 (UTC)
thread_title: This article is about E not E^X

message: Is that E approximation really right?
:Thanks for pointing that out.  I fixed it.--Hypergeometric2F1[a,b,c,x] 05:48, 28 December 2005 (UTC)
thread_title:  E Approximation