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Archive 1 | Archive 2 | Archive 3 | → | Archive 5 |
show a aravege person from dere to here and do it right as u can if u cant do it right then dont do it at all because u will not gte anywhere in your life
Why is the page called "E (mathematical constant)"? I've seen this number named "e" (lowercase) almost everywhere, and the only place, other than Wikipedia, where I've seen "E" (uppercase) is Mathematica. So, I think this page should be renamed to "e (mathematical constant)". -- Fibonacci 00:47, 27 Apr 2004 (UTC)
In The Book on Numbers by John Conway and Richard Guy, the number e is persistently called Napier's number. I know that John Napier more or less discovered logarithms, but is this really the correct name? -- JanHidders
I don't think that's too common; Weisstein lists it as "Napier's Constant", but the main entry is under "e". Encyclopedia Britannica doesn't list "Napier's Number" or "Napier's Constant" at all. Most people call it "the base of the natural logarithm", I believe.
e is still called Euler's number in many texts too introductory to worry about confusion with &gamma (Euler's constant).
Could somebody explain what `e' is useful for? It was always difficult for me to explain it to mathematical newbies.
And could somebody explain ei*π = -1, and why it is so? -- Taw
See The most remarkable formula in the world (where it is poorly explained to the layman, sorry!) -- drj
It's used mainly because it arises "naturally" in calculus, and is related to useful functions (eg., trigonometric and hyperbolic functions). A connection with pi is inevitable, as pi is related (via polar coordinates) to -1 and the trigonometric functions.
Zundark - as far as I know, you should be entitled to claim that you invented the word "miscorrection" :) Great stuff! - MMGB
D'oh! I really need to quit editing pages when I'm so tired I can hardly type straight. At least I got the sum notation definition right...--BlackGriffen
Could this be moved to e (base of natural logarithm), to make it more consistent with other disambiguated titles, and to allow for the pipe trick? -- Oliver P. 00:13 Feb 22, 2003 (UTC)
I think that e (number) would be easily confsed with E numbers The Anome
I think, e should always be spelled e not E...
"The number e is relevant because one can show that the exponential function exp(x) can be written as e^x"
I enjoyed both forms of the expansion (one was removed today). Of course they can be derived from each other, but I still found the patterns that each exhibit interesting. Here are the two forms:
Can we put them both back into the article? Bevo 16:39, 21 Feb 2004 (UTC)
The article says:
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)
I got rid of this again in October 2004, and again today. -- Dominus 02:09, 20 Mar 2005 (UTC)
I think we should add more proofs, eg, that the given continued fraction representation is correct.
I think there needs to be a proof that e^x is it's own derivative. I can do it as far as getting f(x) = b^x then f'(x) = f(x)*f'(0) but don't know how to prove that b = e makes f'(0) = 1 (so that f'(x) = f(x)) Kousu 05:26, 17 June 2006 (UTC)
Just for the record, I removed the bit about the Pyramids and Greeks. It smells of nonsense, was originally added in bold text, and I can't find any other references to either part of it anyway. (And given that the Greeks were not known for their imprecision in mathematics, I can't imagine they'd mistakenly use 2.72 for e if they knew about it.) -- Aponar Kestrel 06:38, 2004 Jul 31 (UTC)
I removed the <big> tags surrounding the approximation of e as this caused the number to be breaked at the resolution of 800x600. If there is a need to include longer expantion of e we should break it ahead of time I think. Two possibilities are:
e ≈ 2. | 71828 18284 59045 23536 02874 71352 |
66249 77572 47093 69995 95749 66968 |
-- filu 13:08, 24 Apr 2005 (UTC)
Not terribly important, but with 30 digits shown, and digit 31 being '6' the number shown would be more accurate if rounded up (and is thus misleading), yet wouldn't show the same digits that longers representations do. (It's just that I assumed that this was the motivation for using 64 digits on the pi page, and was mine for using 64 here.) Frencheigh 00:27, 25 Apr 2005 (UTC)
Just a technical note, currently the article states
As well as being a subjective statement, it is incorrect to someone who knows about the frequency of 10-digit primes. The prime counting function π which has values listed on Prime number theorem, the number of 10 digit primes is π(1010) - π(109) = 455052511 - 50847534 = 404204977. Out of 9000000000 10-digit numbers, this gives an average density of 404204977/9000000000 which is about 4.5%. So we would expect one in 22 randomly-selected 10-digit strings to be prime. It is surprising the first 10-digit prime starts as late as 101 digits in. I am changng the statement for this reason. Andrew Kepert 03:58, 11 May 2005 (UTC)
Let's move this article to Euler's number as that is what this article is about and is much more common than Napier's number.-- MarSch 30 June 2005 16:24 (UTC)
Ed Poor has now moved this page to from E (mathematical constant) to Euler's number. Is everyone ok with that? I have no strong feelings either way, but the move has created a lot redirects which should be fixed (especially the double redirects). I don't know as yet if Ed intends to to do that. I'd be willing to help with the redirects, but i want to be assured that we have a consensus for the name change first. Paul August ☎ 19:43, August 2, 2005 (UTC)
Everyone calls this number e. Calling it anything else is just confusing. Charles Matthews 21:12, 2 August 2005 (UTC)
And the pi page is called that, not Lyudolph's constant or suchlike. Charles Matthews 21:14, 2 August 2005 (UTC)
The name of the thing is Euler's number whether you know this or not. Finding it will happen by going to e and being disambiguated, this is no argument for using a horrible title. e, or e or e is not its name, but simply the symbol used in formulas and should redirect to the name of the object, which is not the same as the symbol. e represent Euler's number in formulas, sometimes as it is also used for other things. I've never heard of Lyudolph's constant, but if that is the correct name, then that the corresponding pages should be treated similarly.-- MarSch 18:10, 14 August 2005 (UTC)
It has been my experience that when mathematicians, physicists, and engineers refer to thsi value, they all call it "e", no one calls it "Euler's number" except in a historical context. You say The name of the thing is Euler's number as an established fact. Pray tell, which international standards body passed on this? Was there a decreee from the God of Newton, the God of Liebnitz, and the God of Cantor? can you site any source that says this is the name of this concept and no other name is valid, or anythign of the sort? DES (talk) 20:01, 14 August 2005 (UTC)
I agree with DESiegel. The name is just e. I've heard the locution "Euler's number" but it's rarely used. Yes, e is sometimes used to mean other things, but then so is π. Move to "e (number)" or "e (mathematical constant)", and make the others redirects. -- Trovatore 21:15, 14 August 2005 (UTC)
I can't see any reason for this move. If you hate the technical limitation template for some mysterious reason I can't imagine, this page'd better be called "base of natural logarithms", but IMO "E (mathematical constant)" is OK and should remain.-- Army1987 21:37, 14 August 2005 (UTC)
I am strongly opposed to this move. I agree with Charles Matthews's and DESiegel's comments, above. -- Dominus 15:06, 15 August 2005 (UTC)
Remarkable Euler was one of the most prolific mathematicians ever, and has quite enough things named after him. Perhaps it's a difference of cultures — whether of schools or languages or countries I cannot say — but I am unaccustomed to hearing my old friend e referred to as Euler's anything. I am very much accustomed to hearing the number γ referred to as "Euler's constant". Both are numbers and both are constants, so having distinct meanings would be awful. (That's never stopped mathematicians before, but still…) Given the redirect machinery, the decision makes little difference technically; if I'm wrong, please correct me. So I base my decision on other grounds: Calling the page "Euler's number" seems NPOV in light of this discussion, since e may or may not go by that name, depending upon who you ask; therefore the page must remain at "e (mathematical constant)". KSmrq 12:46, 2005 August 16 (UTC)
I don't get how that would equal e. I'm trying to think about it... if n tends to infinity, 1 / n tends to zero... which leaves just 1^n, but surely that'll just equal 1? I don't get it...
I prefer the definition of e via the integral of 1/x. It makes much more sense. Deskana 11:17, 27 August 2005 (UTC)
I have another question then. Why do those approach e? I understand the integral one, because when you do the integral you get ln(t), putting e and 1 in you get ln(e) - ln(1) which of course equals 1. Why do the others work? Deskana 10:05, 28 August 2005 (UTC)
The first definition of e says "The limit". The second one says "The sum of the infinite series". The second one is as much a limit of a sequence as the first one is.
Kprateek88
14:01, 7 September 2006 (UTC)
I disagree with the statement calling "e" (along with "pi" and "i") some of the "most important" numbers. I won't raise a POV argument (though one conceivably might)... just this:
Tell me which of these numbers is less important: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15...
I defy anyone to make a case that "e" is anywhere near as important as any integer from 0 up to... oh, I don't know... a million? (probably more than that) ...
I don't know how you'd rephrase that--I called them "special numbers", but that's probably not too accurate. If anyone knows the name for these types of numbers, that'd be awesome. Matt Yeager 06:31, 11 November 2005 (UTC)
Hmm, alright, I see what you're saying. But then again, if all 2 is is (1+1), then all e is is (1/(1-1)! + 1/1! + 1/(1+1)! + 1/(1+1+1)! ... ), right? And wouldn't i be the sq. root of (1-1-1)? In that case, you could make a case that so long as you have all of the mathematical functions at your disposal, then with the aid of just one non-zero number, you could create all the others (except π (to the best of my knowledge), and maybe some other "weird" numbers). All the numbers we've mentioned (including e) can be picked up from, say, 7, by defining 1 as 7/7, defining 2 as 7/7 + 7/7, etc.
The point of all this is that e is just a number that can be derived from other numbers, just like 2, 3, 4, 5, etc. And if we're listing functions, I guarantee that I can come up with more common uses for the number 2 than anyone can for e.
What I'm trying to say is, there needs to be some sort of qualifying term applied to that first statement in the article. Right? Matt Yeager 22:23, 13 November 2005 (UTC)
Hmm... your logic doesn't work. You're comparing apples to oranges. Of course all the mathematicians in the world produce more than authors of K-12 math books. But the output of all the mathematicians in the world doesn't even scratch the surface of how great the output is of all the people in the world, most of which have no idea what e is but use 2 every day, so 2 wins if we compare general output. If we compare books (that are actually used), and the usage of those books, I believe 2 wins again, though that's debatable. Only when you compare the "material" output of mathematicians (whether anyone cares about it and reads it or not) to the number of books put out by K-12 authors (apples to oranges) does e appear to win.
The idea that your source supports your argument is questionable, too. All the site says is that e is the 2nd-most important constant (oh look, I just used 2). Is a constant the same as a number? Constant states that there really isn't a good definition of what a constant is, so it's hard to tell. The site you provided (when you click on the "constant" link) says that "In this work, the term 'constant' is generally reserved for real nonintegral numbers of interest" [3]. Dubious at best. Matt Yeager 03:57, 14 November 2005 (UTC)
Of course to a certain extent the opinion of which numbers are more important is biased, but let me try a brief explanation. 1 is very important because it is the foundation of Peano arithmetic, which allows one to build the natural numbers, and from there the real numbers. The number i allows for the extension to the complex plane. π is a number which fascinated people from antiquity. The number e is at the base of natural logarithms which revolutionized calculations and lead to the invention of the slide rule.
All these numbers, 1, i, π and e produced a seismic shift in a sence in their time in mathematics. Think of the controversy/advances when it was realized that starting with basic axioms of counting you can build up the real numbers, that i is not just a magic imaginary number and that it allows solving any equations, that the circle cannot be squared, and that e does not solve any equation with polynomial coefficients.
By the way, please note that you have been stepping the bounds of a civilized debate lately. Repeatedly reverting this article does not help you make a point. Oleg Alexandrov ( talk) 07:17, 16 November 2005 (UTC)
One at a time.
Oh and by the way... I'm sorry if I'm being a pain--I definitely see how my comment last night was a little over the line. Matt Yeager 21:04, 16 November 2005 (UTC)
Works for me. I don't feel that any contradictory quotes are necessary, though. I'm going to try and fix up the formatting, though--the page looks a little off as is. Matt Yeager 06:17, 17 November 2005 (UTC)
Here's a popularity test:
Not to be taken too seriously ;-) - Fredrik | t c 18:26, 17 November 2005 (UTC)
Hm, that's very different from the results for Googlefight: pi "most important number", vs. e "most important number"
1. The text should say
2. The text should say:
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)
Hypergeometric, please do not mark deletions of text as minor. - lethe talk 09:49, 22 December 2005 (UTC)
If you don't want to comply with my request, that is of course your prerogative. It is simply a courtesy to others who have a vested interest in the article you are editing. If you use it properly, it saves those others time and effort. If you abuse it, it costs us extra time and effort. I would prefer it if I could consider you a trusted editor, whom I don't feel obliged to monitor. I could spend more time editing, and less time policing and tidying. But please, there's no need to impugn my value as a contributor. I didn't mean to offend you with my request. I do not appreciate the implication that I "sit around and do nothing". Just because I'm not editing this article doesn't mean that A. I don't have a stake in what happens to this article, nor does it mean that B. I'm not doing anything at all. I have this week done a fair amount of work on for example axiom of replacement, boundary (topology), affine space, order topology. I also participate in group discussions, monitor my watchlist, and answer questions at WP:RD/Maths, and do general nitpicking and maintainence. But why am I defending my contributions against you? Bollocks. - lethe talk 15:27, 22 December 2005 (UTC)
Thanks for cleaning up my edits whoever did that. I retract my comments as I went a bit out of line. I'm getting my old EDM from my parents' house this Chistmas so I'll be referring to it for some contribs. By the way this is Hypergeometric Im just using my parents comp. -- Hypergeometric2F1[a,b,c,x] (signed by Oleg Alexandrov ( talk))
Is that E approximation really right?
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 | Archive 3 | → | Archive 5 |
show a aravege person from dere to here and do it right as u can if u cant do it right then dont do it at all because u will not gte anywhere in your life
Why is the page called "E (mathematical constant)"? I've seen this number named "e" (lowercase) almost everywhere, and the only place, other than Wikipedia, where I've seen "E" (uppercase) is Mathematica. So, I think this page should be renamed to "e (mathematical constant)". -- Fibonacci 00:47, 27 Apr 2004 (UTC)
In The Book on Numbers by John Conway and Richard Guy, the number e is persistently called Napier's number. I know that John Napier more or less discovered logarithms, but is this really the correct name? -- JanHidders
I don't think that's too common; Weisstein lists it as "Napier's Constant", but the main entry is under "e". Encyclopedia Britannica doesn't list "Napier's Number" or "Napier's Constant" at all. Most people call it "the base of the natural logarithm", I believe.
e is still called Euler's number in many texts too introductory to worry about confusion with &gamma (Euler's constant).
Could somebody explain what `e' is useful for? It was always difficult for me to explain it to mathematical newbies.
And could somebody explain ei*π = -1, and why it is so? -- Taw
See The most remarkable formula in the world (where it is poorly explained to the layman, sorry!) -- drj
It's used mainly because it arises "naturally" in calculus, and is related to useful functions (eg., trigonometric and hyperbolic functions). A connection with pi is inevitable, as pi is related (via polar coordinates) to -1 and the trigonometric functions.
Zundark - as far as I know, you should be entitled to claim that you invented the word "miscorrection" :) Great stuff! - MMGB
D'oh! I really need to quit editing pages when I'm so tired I can hardly type straight. At least I got the sum notation definition right...--BlackGriffen
Could this be moved to e (base of natural logarithm), to make it more consistent with other disambiguated titles, and to allow for the pipe trick? -- Oliver P. 00:13 Feb 22, 2003 (UTC)
I think that e (number) would be easily confsed with E numbers The Anome
I think, e should always be spelled e not E...
"The number e is relevant because one can show that the exponential function exp(x) can be written as e^x"
I enjoyed both forms of the expansion (one was removed today). Of course they can be derived from each other, but I still found the patterns that each exhibit interesting. Here are the two forms:
Can we put them both back into the article? Bevo 16:39, 21 Feb 2004 (UTC)
The article says:
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)
I got rid of this again in October 2004, and again today. -- Dominus 02:09, 20 Mar 2005 (UTC)
I think we should add more proofs, eg, that the given continued fraction representation is correct.
I think there needs to be a proof that e^x is it's own derivative. I can do it as far as getting f(x) = b^x then f'(x) = f(x)*f'(0) but don't know how to prove that b = e makes f'(0) = 1 (so that f'(x) = f(x)) Kousu 05:26, 17 June 2006 (UTC)
Just for the record, I removed the bit about the Pyramids and Greeks. It smells of nonsense, was originally added in bold text, and I can't find any other references to either part of it anyway. (And given that the Greeks were not known for their imprecision in mathematics, I can't imagine they'd mistakenly use 2.72 for e if they knew about it.) -- Aponar Kestrel 06:38, 2004 Jul 31 (UTC)
I removed the <big> tags surrounding the approximation of e as this caused the number to be breaked at the resolution of 800x600. If there is a need to include longer expantion of e we should break it ahead of time I think. Two possibilities are:
e ≈ 2. | 71828 18284 59045 23536 02874 71352 |
66249 77572 47093 69995 95749 66968 |
-- filu 13:08, 24 Apr 2005 (UTC)
Not terribly important, but with 30 digits shown, and digit 31 being '6' the number shown would be more accurate if rounded up (and is thus misleading), yet wouldn't show the same digits that longers representations do. (It's just that I assumed that this was the motivation for using 64 digits on the pi page, and was mine for using 64 here.) Frencheigh 00:27, 25 Apr 2005 (UTC)
Just a technical note, currently the article states
As well as being a subjective statement, it is incorrect to someone who knows about the frequency of 10-digit primes. The prime counting function π which has values listed on Prime number theorem, the number of 10 digit primes is π(1010) - π(109) = 455052511 - 50847534 = 404204977. Out of 9000000000 10-digit numbers, this gives an average density of 404204977/9000000000 which is about 4.5%. So we would expect one in 22 randomly-selected 10-digit strings to be prime. It is surprising the first 10-digit prime starts as late as 101 digits in. I am changng the statement for this reason. Andrew Kepert 03:58, 11 May 2005 (UTC)
Let's move this article to Euler's number as that is what this article is about and is much more common than Napier's number.-- MarSch 30 June 2005 16:24 (UTC)
Ed Poor has now moved this page to from E (mathematical constant) to Euler's number. Is everyone ok with that? I have no strong feelings either way, but the move has created a lot redirects which should be fixed (especially the double redirects). I don't know as yet if Ed intends to to do that. I'd be willing to help with the redirects, but i want to be assured that we have a consensus for the name change first. Paul August ☎ 19:43, August 2, 2005 (UTC)
Everyone calls this number e. Calling it anything else is just confusing. Charles Matthews 21:12, 2 August 2005 (UTC)
And the pi page is called that, not Lyudolph's constant or suchlike. Charles Matthews 21:14, 2 August 2005 (UTC)
The name of the thing is Euler's number whether you know this or not. Finding it will happen by going to e and being disambiguated, this is no argument for using a horrible title. e, or e or e is not its name, but simply the symbol used in formulas and should redirect to the name of the object, which is not the same as the symbol. e represent Euler's number in formulas, sometimes as it is also used for other things. I've never heard of Lyudolph's constant, but if that is the correct name, then that the corresponding pages should be treated similarly.-- MarSch 18:10, 14 August 2005 (UTC)
It has been my experience that when mathematicians, physicists, and engineers refer to thsi value, they all call it "e", no one calls it "Euler's number" except in a historical context. You say The name of the thing is Euler's number as an established fact. Pray tell, which international standards body passed on this? Was there a decreee from the God of Newton, the God of Liebnitz, and the God of Cantor? can you site any source that says this is the name of this concept and no other name is valid, or anythign of the sort? DES (talk) 20:01, 14 August 2005 (UTC)
I agree with DESiegel. The name is just e. I've heard the locution "Euler's number" but it's rarely used. Yes, e is sometimes used to mean other things, but then so is π. Move to "e (number)" or "e (mathematical constant)", and make the others redirects. -- Trovatore 21:15, 14 August 2005 (UTC)
I can't see any reason for this move. If you hate the technical limitation template for some mysterious reason I can't imagine, this page'd better be called "base of natural logarithms", but IMO "E (mathematical constant)" is OK and should remain.-- Army1987 21:37, 14 August 2005 (UTC)
I am strongly opposed to this move. I agree with Charles Matthews's and DESiegel's comments, above. -- Dominus 15:06, 15 August 2005 (UTC)
Remarkable Euler was one of the most prolific mathematicians ever, and has quite enough things named after him. Perhaps it's a difference of cultures — whether of schools or languages or countries I cannot say — but I am unaccustomed to hearing my old friend e referred to as Euler's anything. I am very much accustomed to hearing the number γ referred to as "Euler's constant". Both are numbers and both are constants, so having distinct meanings would be awful. (That's never stopped mathematicians before, but still…) Given the redirect machinery, the decision makes little difference technically; if I'm wrong, please correct me. So I base my decision on other grounds: Calling the page "Euler's number" seems NPOV in light of this discussion, since e may or may not go by that name, depending upon who you ask; therefore the page must remain at "e (mathematical constant)". KSmrq 12:46, 2005 August 16 (UTC)
I don't get how that would equal e. I'm trying to think about it... if n tends to infinity, 1 / n tends to zero... which leaves just 1^n, but surely that'll just equal 1? I don't get it...
I prefer the definition of e via the integral of 1/x. It makes much more sense. Deskana 11:17, 27 August 2005 (UTC)
I have another question then. Why do those approach e? I understand the integral one, because when you do the integral you get ln(t), putting e and 1 in you get ln(e) - ln(1) which of course equals 1. Why do the others work? Deskana 10:05, 28 August 2005 (UTC)
The first definition of e says "The limit". The second one says "The sum of the infinite series". The second one is as much a limit of a sequence as the first one is.
Kprateek88
14:01, 7 September 2006 (UTC)
I disagree with the statement calling "e" (along with "pi" and "i") some of the "most important" numbers. I won't raise a POV argument (though one conceivably might)... just this:
Tell me which of these numbers is less important: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15...
I defy anyone to make a case that "e" is anywhere near as important as any integer from 0 up to... oh, I don't know... a million? (probably more than that) ...
I don't know how you'd rephrase that--I called them "special numbers", but that's probably not too accurate. If anyone knows the name for these types of numbers, that'd be awesome. Matt Yeager 06:31, 11 November 2005 (UTC)
Hmm, alright, I see what you're saying. But then again, if all 2 is is (1+1), then all e is is (1/(1-1)! + 1/1! + 1/(1+1)! + 1/(1+1+1)! ... ), right? And wouldn't i be the sq. root of (1-1-1)? In that case, you could make a case that so long as you have all of the mathematical functions at your disposal, then with the aid of just one non-zero number, you could create all the others (except π (to the best of my knowledge), and maybe some other "weird" numbers). All the numbers we've mentioned (including e) can be picked up from, say, 7, by defining 1 as 7/7, defining 2 as 7/7 + 7/7, etc.
The point of all this is that e is just a number that can be derived from other numbers, just like 2, 3, 4, 5, etc. And if we're listing functions, I guarantee that I can come up with more common uses for the number 2 than anyone can for e.
What I'm trying to say is, there needs to be some sort of qualifying term applied to that first statement in the article. Right? Matt Yeager 22:23, 13 November 2005 (UTC)
Hmm... your logic doesn't work. You're comparing apples to oranges. Of course all the mathematicians in the world produce more than authors of K-12 math books. But the output of all the mathematicians in the world doesn't even scratch the surface of how great the output is of all the people in the world, most of which have no idea what e is but use 2 every day, so 2 wins if we compare general output. If we compare books (that are actually used), and the usage of those books, I believe 2 wins again, though that's debatable. Only when you compare the "material" output of mathematicians (whether anyone cares about it and reads it or not) to the number of books put out by K-12 authors (apples to oranges) does e appear to win.
The idea that your source supports your argument is questionable, too. All the site says is that e is the 2nd-most important constant (oh look, I just used 2). Is a constant the same as a number? Constant states that there really isn't a good definition of what a constant is, so it's hard to tell. The site you provided (when you click on the "constant" link) says that "In this work, the term 'constant' is generally reserved for real nonintegral numbers of interest" [3]. Dubious at best. Matt Yeager 03:57, 14 November 2005 (UTC)
Of course to a certain extent the opinion of which numbers are more important is biased, but let me try a brief explanation. 1 is very important because it is the foundation of Peano arithmetic, which allows one to build the natural numbers, and from there the real numbers. The number i allows for the extension to the complex plane. π is a number which fascinated people from antiquity. The number e is at the base of natural logarithms which revolutionized calculations and lead to the invention of the slide rule.
All these numbers, 1, i, π and e produced a seismic shift in a sence in their time in mathematics. Think of the controversy/advances when it was realized that starting with basic axioms of counting you can build up the real numbers, that i is not just a magic imaginary number and that it allows solving any equations, that the circle cannot be squared, and that e does not solve any equation with polynomial coefficients.
By the way, please note that you have been stepping the bounds of a civilized debate lately. Repeatedly reverting this article does not help you make a point. Oleg Alexandrov ( talk) 07:17, 16 November 2005 (UTC)
One at a time.
Oh and by the way... I'm sorry if I'm being a pain--I definitely see how my comment last night was a little over the line. Matt Yeager 21:04, 16 November 2005 (UTC)
Works for me. I don't feel that any contradictory quotes are necessary, though. I'm going to try and fix up the formatting, though--the page looks a little off as is. Matt Yeager 06:17, 17 November 2005 (UTC)
Here's a popularity test:
Not to be taken too seriously ;-) - Fredrik | t c 18:26, 17 November 2005 (UTC)
Hm, that's very different from the results for Googlefight: pi "most important number", vs. e "most important number"
1. The text should say
2. The text should say:
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)
Hypergeometric, please do not mark deletions of text as minor. - lethe talk 09:49, 22 December 2005 (UTC)
If you don't want to comply with my request, that is of course your prerogative. It is simply a courtesy to others who have a vested interest in the article you are editing. If you use it properly, it saves those others time and effort. If you abuse it, it costs us extra time and effort. I would prefer it if I could consider you a trusted editor, whom I don't feel obliged to monitor. I could spend more time editing, and less time policing and tidying. But please, there's no need to impugn my value as a contributor. I didn't mean to offend you with my request. I do not appreciate the implication that I "sit around and do nothing". Just because I'm not editing this article doesn't mean that A. I don't have a stake in what happens to this article, nor does it mean that B. I'm not doing anything at all. I have this week done a fair amount of work on for example axiom of replacement, boundary (topology), affine space, order topology. I also participate in group discussions, monitor my watchlist, and answer questions at WP:RD/Maths, and do general nitpicking and maintainence. But why am I defending my contributions against you? Bollocks. - lethe talk 15:27, 22 December 2005 (UTC)
Thanks for cleaning up my edits whoever did that. I retract my comments as I went a bit out of line. I'm getting my old EDM from my parents' house this Chistmas so I'll be referring to it for some contribs. By the way this is Hypergeometric Im just using my parents comp. -- Hypergeometric2F1[a,b,c,x] (signed by Oleg Alexandrov ( talk))
Is that E approximation really right?