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 4 | Archive 5 |
Is it possible to explain e in any meaningful sense to a layman, rather than just it being the 'base of the natural logarithm function'? That still doesn't mean a whole lot to the average person! —The preceding unsigned comment was added by 62.255.0.7 ( talk • contribs) . 12:06, January 1, 2005 (UTC)
The last infinite series listed in this article is
But for k=0 we have division by zero (and also the square root of a negative number). I think the sum should start from k=1. Can anyone confirm? Eric119 04:08, 2 January 2006 (UTC)
A friend of mine wrote a little computer program that can make an article title begin with a lower case letter. Is anyone interested in changing the title of this article from E (mathematical constant) to e (mathematical constant)? Uncle Ed 13:16, 10 January 2006 (UTC)
... would generally include "0" and "1". As per the "famous five" of Euler's identity, indeed. I won't edit this directly in case anyone's upset, y'all just having had a poll, n'stuff. :) Alai 08:54, 30 January 2006 (UTC)
I'd say 1 is important because it a generator of Z, not because it is the multiplicative identity. More importantly though, do people really care that 0 and 1 are the additive/multiplicative identity (do non-mathheads know what this means?) when they are reading an article about e? — Ruud 19:23, 31 January 2006 (UTC)
There are a number of more complicated concepts in math that have been explained in laymen's terms. The problem with the e discussion is that no attempt is made to explain what "natural" means. It is either arrogant or wrong to say that no one si or will be interested in e if they are not concerned with pure math, physics, etc.
("Also, questions are more likely to be seen when they get proper headings and go to the bottom of the page, which this did not. - lethe talk + 19:53, 3 February 2006 (UTC)"
Thanks for the image. A suggestion. I think the fonts on the axes should be made much bigger, the lines a bit thicker, and a few colors would not hurt. I would think of something of the style at subgradient (yeah, my own picture, so I am bragging here :) Oleg Alexandrov ( talk) 04:02, 7 February 2006 (UTC)
E is also the second most found word on google.
I don't like the current ℮ (mathematical constant) title. I would think moving it back to E (mathematical constant) would be better. Comments? Oleg Alexandrov ( talk) 23:31, 26 February 2006 (UTC)
I think Martin Gardner mentioned some mnemonics for recalling the first several digits of e. The only one that springs to mind is "I'm forming a mnemonic to remember a constant in analysis", the words of which have 2, 7, 1, 8, 2, 8, 1, 8, 2 and 8 letters. I don't know if it's worth including in the article, but I thought it was kind of cool. Kensson 16:09, 8 March 2006 (UTC)Kensson
In my oppinion, the natural occurences of e section of the article sould be creaded and expanded. What are your oppinions on this topic?--BorisFromStockdale 21:09, 9 March 2006 (UTC)
Should we show that L'Hopital's Rule is required in order to actually find the limit of this expression? As it is now, it would just come out to 1^infinity. - Christopher 07:47, 10 March 2006 (UTC)
So, where thrn did come from? Surely, Bernoulli didn't one day randomly decide to find the limit of this function. - Christopher 18:43, 14 March 2006 (UTC)
This page was moved to mathematical constant e. I don't support such a move, so I've moved it back to e (mathematical constant). If and when a consensus should arise for another name, then I won't oppose. - lethe talk + 09:04, 15 March 2006 (UTC)
Is the discussion about the lack of "layman terms" for e one that can be solved by adding an example to the article text? A friend taught me e by using an (imagined) drum that contained 1 liter of water, trying to add water to the container at an initial rate of 1 l per second, for one second. Now, impossibilities arise when, in infinitely small increments, more water is added to the rate as time goes by. After one second, you have what can be rounded off to 2,7 liters of water, but which in maths will always be an endless number. For physics: Should one assume there is a definite particle that all is made of, and that the observer was in posession of instruments to count every single added particle, it still wouldn't limit the end value e. For that, you need (granted I understood this right - I may have made a huge fool out of myself just now) a definite timeunit, say a hundredth of a second. As there is none, e is considered endless. Sorry if this is redundant, just trying to be constructive and such.
Someone named Hiiiiiiii recently added one more digit. The text claimed 29 digits, so adding another made the text incorrect. I fixed the text, and clarified that it's truncating, not rounding (though maybe we should prefer to round up?). Furthermore, I added the digit back, becaues I seem to remember my old fashioned tables of numbers format things in blocks of five digits aligned to the decimal point. I could be misremembering though. - lethe talk + 18:08, 7 April 2006 (UTC)
The page was moved a second time to ℮ (mathematical constant). I guess there is some support for the idea, but I'm sure also some opposition. I've moved back. - lethe talk + 20:31, 11 April 2006 (UTC)
I've protected the page from being moved. These semi-clever unicode-hacks are starting to become a bit tiring by now and it really shouldn't be moved without a discussion first. — Ruud 16:55, 12 April 2006 (UTC)
Isn't the curvature of e used in erecting structures? I remember learning that a parabolic shape wouldn't be as good as an e shape. Anyone have any information on this? 71.250.59.37 20:22, 3 May 2006 (UTC)
Not sure about others, but this sounds a bit odd to me - how can a number be both truncated and rounded? I would suggest "or" instead, or preferably replace with "correct to 20 decimal places"? Madmath789 13:16, 30 May 2006 (UTC)
Is there any good reason why the horizontal and vertical axes of the Image:E-ruud.png are not drawn to the same scale? Evercat 20:12, 9 June 2006 (UTC)
The text cites A005131 as the simple continued fraction of e, but OEIS:A003417 says it is. The latter looks more reasonable to me. Then the question is, what is OEIS:A005131? Lee S. Svoboda tɑk 22:11, 26 August 2006 (UTC)
I added a third generalized continued fraction that converges far more quickly than the first two. It corresponds to the series
1/1, 3/1, 19/7, 193/71, 2721/1001, ...
Each convergent adds 2-3 decimal digits of precision to its predcessor.
I also added a general formula for e^(2m/n) for |m|,n = 1,2,3,...; however, convergence slows as |m| increases in value. When m=1 and n=2 you get the formula for e.
Glenn L
The graph comparing f(x)=e^x to f'(x) is nice, but a little confusing, if only because x=.7 (whatever it is, don't have calculator handy), which gives f(x) = 2. Which is nice, but not entirely evident unless you know to look for it. Perhaps showing x=1 would help, and showing the equation "e^(.7whatever) = 2, which is the slope at that point, and e^1 = 1, which is the slope there." Perhaps even more explicitly labelling the slope of 2 would help (either with a direct label, or an old middleschool "rise over run" triangle, showing that it goes up 2 for every 1 over). And, I may be splitting hairs, but it seems like the line for e^x should be bolded, or that the f' line should not be given equal weight. I say this just because it is the first (and only) graph on the page, so it is doing double duty: showing the function e^x (very important) and showing that that derivative of e^x equals e^x (important, but less important than showing that function itself). Sir Isaac Lime 20:13, 19 September 2006 (UTC)
Reinstated my paragraph on APR (interest rates) after it was completely deleted by RandomP on the grounds that he didn't know what "percentage rate" meant. Expanded the text slightly to clarify, but a really detailed explanation of APR/interest probably belongs in an article on that subject. -- DarelRex 13:34, 26 September 2006 (UTC)
This is not a personal attack; please do not repeatedly delete my entire post on the grounds that it needs a tiny fix. I have now reposted it (again) with an extra sentence that hopefully alleviates the problem as best as I understand it from your above criticism. If further modification is necessary, please advise or revise instead of axing the whole thing again and again. Thanks. -- DarelRex 13:56, 26 September 2006 (UTC)
e is also relevant to measuring the difference between linear growth and exponential growth. If the doubling period for a process of exponential growth is estimated by linear approximation, the actual growth factor will be e after that time.
For example, assume that a bank continuously compounds interest, and we start with $1 in the bank, with current interest payments at a rate of $1/year. In order to calculate the annualised percentage rate, we might consider this rate to remain constant, and estimate the doubling period at a year — and thus, the annualised percentage rate at 100.
However, taking compound interest into account, we see that after a year, the account balance is $e, for an annualised percentage rate of approximately 172, much higher than our original estimate.
So if any "crazy" person might lift something out of context and use it to mispresent something else, then it has to be entirely removed? You are obviously determined to keep my paragraph out, so I will not repost it, even though I do not understand your criticisms. Your suggestion of what to replace my paragraph with will surely obfuscate its meaning to all but the most mathematically advanced readers. I give up; you win. -- 155.188.247.6 14:27, 26 September 2006 (UTC)
I think a lot of people would get more out of a "real world" example, such as e being involved in the difference between simple and compound interest, than all those very abstract equations. -- Hugh7 08:52, 24 January 2007 (UTC)
I think that a picture showing the tangent line at 1, instead of 2 would ilustrate the point much more clearly... a slope of one is easier to see. 160.39.168.58 04:25, 11 December 2006 (UTC)
Does that mean the additive identity is 0 and the multiplicative identity is 1, or does it mean "the [actions] of addition and multiplication and the numbers 0 and 1"? Could someone please clarify this on the page. -- Hugh7 08:44, 24 January 2007 (UTC)
If you do not know that zero is the additive identity and that one is the multiplicative identity, then this article is beyond your level. JRSpriggs 11:57, 24 January 2007 (UTC)
Right now it's listed as the sum of (1/n!) from 0 to infinity; this doesn't seem to be right because 1/0! is 1, or am I mistaken? (I had learned before that 0! is a special case equal to 1) Since 1/0! + 1/1! is already 2, the next few numbers (2 through 6, I think) make the value pass 1... could somebody clear this up for me? Robinson0120 02:04, 28 January 2007 (UTC)
Ruud's graph showing the tangent to e^x at x=0 was replaced by a nice SVG graph with a tangent drawn at a different place, and the simple definition that e is the unique number such that the slope of the tangent to e^x at 0 is 1 was replaced by the much more scary-sounding (equivalent but over-specified) definition that e is the unique number such that the slope of the tangent to e^x is e^x for all x. Why? Can we modify the SVG and the definition back to the much simpler version, such that the graph actually illustrates the condition? We could also draw some light curves for 2^x and 4^x just to illustrate that they have different slope, not 1, at x=0. Dicklyon 03:17, 28 January 2007 (UTC)
Dicklyon decided to revert rather than follow Wikipedia rules on reverting. Rather than give the editer the benefit of the doubt, he reverted rather than fix it. This is a violation of the revert policy. Please help if you can. —The preceding unsigned comment was added by 172.163.172.47 ( talk) 20:47, 4 February 2007 (UTC).
To EJ: I changed the indefinite integral for e to the definite integral form:
because it has a unique solution and it can be used to generate the series expression for e. You replaced it with:
which appears superficially to be a definite integral, but actually is ambiguous and equivalent to the indefinite integral form from which I was trying to get away. Nor is it simpler as you said it was. It includes an implied limit as the lower bound goes to negative infinity, which makes it more complex than my version. JRSpriggs 08:46, 6 February 2007 (UTC)
I asked EJ a similar question on his talk page yesterday, JR. Here's his response.
- Why is the integral improper? AFAICS, it is a usual convergent Lebesgue integral of a nonnegative function, there is no need to go through the limit .
- Anyway, I'm notoriously bad at estimating the level of mathematical sophistication needed for understanding particular problems, so if you think the original formula is easier, do not hesitate to revert. However, I should point out that the original formula also relies on a convention which might or might not be clear to less sophisticated readers, namely for negative x. -- EJ 15:22, 5 February 2007 (UTC)
While I have to concede his point (in a measure-theoretic sense, there are no improper integrals), I don't think the typical reader of Wikipedia is up to speed on the fine points that distinguish the many possible definitions of an "integral" from one another. So I'm reinstating JR's version of the formula, because I think it's better for our target audience. DavidCBryant 12:22, 6 February 2007 (UTC)
DavidCBryant, your rewrite of this section has at least three problems that I see: 1. You disconnected the reference to the math formula that is involved. You either need to refer to the History or Definition section above, or repeat the formula explicitly. 2. You introduced the informal imperative style "Think about an account...". Not good. 3. You dropped the connection to the illustration. Please work on it some more. Dicklyon 18:11, 6 February 2007 (UTC)
I know very little about mathmatical concepts such as this, so I don't feel very comfortable editing the article, but it's my understanding that e is an irrational number, and this doesn't come across very clearly in the article. Does anyone object to this being mentioned in the opening paragraph? I think it would help expalin why the number is not shown in its entirety. - R. fiend 18:44, 10 February 2007 (UTC)
User:Hypergeometric2F1(a,b,c,x) put in a formula back on 21 December 2005 that had previously been repeatedly inserted by a user who called it "Keller's Expression", presumably after himself. This self-promotion had been removed several times before. Today I removed it yet again. -- Dominus 16:33, 15 February 2007 (UTC)
Let us delete the section on mnemonics, "Remembering the digits of e". It adds nothing of value. JRSpriggs 11:18, 28 February 2007 (UTC)
I would disagree. wikipedia guidelines suggest space should be awarded based on interest and importance. remembering the digits of e both allows people to better remember e (which is important)and while it is hard to prove something interesting the methods based upon myself and my math class 100 of people were mildly (or more) interested in the methods for remembering particularly the Andrew Jackson portion Beckboyanch 08:30, 3 March 2007 (UTC)
Hi! Is there a way to calculate some incorrect but approximate value of e using some sort of finite fraction/series? (Like for PI, we have 22/7 or 355/311). If there is, I would really like to add it to the article.-- Scheibenzahl 20:23, 9 March 2007 (UTC)
The reason for the difference is that the (simple) continued fraction expression for π [3; 7, 15, 1, 292...] has no obvious pattern, while that for e [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1...] *does* have an obvious pattern. The best approximations for e involve truncation after terms 2, 5, 8, 11... yielding 3/1, 19/7, 193/71, 2721/1001... as described in my previous entry in this discussion. Glenn L 15:12, 27 May 2007 (UTC)
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 4 | Archive 5 |
Is it possible to explain e in any meaningful sense to a layman, rather than just it being the 'base of the natural logarithm function'? That still doesn't mean a whole lot to the average person! —The preceding unsigned comment was added by 62.255.0.7 ( talk • contribs) . 12:06, January 1, 2005 (UTC)
The last infinite series listed in this article is
But for k=0 we have division by zero (and also the square root of a negative number). I think the sum should start from k=1. Can anyone confirm? Eric119 04:08, 2 January 2006 (UTC)
A friend of mine wrote a little computer program that can make an article title begin with a lower case letter. Is anyone interested in changing the title of this article from E (mathematical constant) to e (mathematical constant)? Uncle Ed 13:16, 10 January 2006 (UTC)
... would generally include "0" and "1". As per the "famous five" of Euler's identity, indeed. I won't edit this directly in case anyone's upset, y'all just having had a poll, n'stuff. :) Alai 08:54, 30 January 2006 (UTC)
I'd say 1 is important because it a generator of Z, not because it is the multiplicative identity. More importantly though, do people really care that 0 and 1 are the additive/multiplicative identity (do non-mathheads know what this means?) when they are reading an article about e? — Ruud 19:23, 31 January 2006 (UTC)
There are a number of more complicated concepts in math that have been explained in laymen's terms. The problem with the e discussion is that no attempt is made to explain what "natural" means. It is either arrogant or wrong to say that no one si or will be interested in e if they are not concerned with pure math, physics, etc.
("Also, questions are more likely to be seen when they get proper headings and go to the bottom of the page, which this did not. - lethe talk + 19:53, 3 February 2006 (UTC)"
Thanks for the image. A suggestion. I think the fonts on the axes should be made much bigger, the lines a bit thicker, and a few colors would not hurt. I would think of something of the style at subgradient (yeah, my own picture, so I am bragging here :) Oleg Alexandrov ( talk) 04:02, 7 February 2006 (UTC)
E is also the second most found word on google.
I don't like the current ℮ (mathematical constant) title. I would think moving it back to E (mathematical constant) would be better. Comments? Oleg Alexandrov ( talk) 23:31, 26 February 2006 (UTC)
I think Martin Gardner mentioned some mnemonics for recalling the first several digits of e. The only one that springs to mind is "I'm forming a mnemonic to remember a constant in analysis", the words of which have 2, 7, 1, 8, 2, 8, 1, 8, 2 and 8 letters. I don't know if it's worth including in the article, but I thought it was kind of cool. Kensson 16:09, 8 March 2006 (UTC)Kensson
In my oppinion, the natural occurences of e section of the article sould be creaded and expanded. What are your oppinions on this topic?--BorisFromStockdale 21:09, 9 March 2006 (UTC)
Should we show that L'Hopital's Rule is required in order to actually find the limit of this expression? As it is now, it would just come out to 1^infinity. - Christopher 07:47, 10 March 2006 (UTC)
So, where thrn did come from? Surely, Bernoulli didn't one day randomly decide to find the limit of this function. - Christopher 18:43, 14 March 2006 (UTC)
This page was moved to mathematical constant e. I don't support such a move, so I've moved it back to e (mathematical constant). If and when a consensus should arise for another name, then I won't oppose. - lethe talk + 09:04, 15 March 2006 (UTC)
Is the discussion about the lack of "layman terms" for e one that can be solved by adding an example to the article text? A friend taught me e by using an (imagined) drum that contained 1 liter of water, trying to add water to the container at an initial rate of 1 l per second, for one second. Now, impossibilities arise when, in infinitely small increments, more water is added to the rate as time goes by. After one second, you have what can be rounded off to 2,7 liters of water, but which in maths will always be an endless number. For physics: Should one assume there is a definite particle that all is made of, and that the observer was in posession of instruments to count every single added particle, it still wouldn't limit the end value e. For that, you need (granted I understood this right - I may have made a huge fool out of myself just now) a definite timeunit, say a hundredth of a second. As there is none, e is considered endless. Sorry if this is redundant, just trying to be constructive and such.
Someone named Hiiiiiiii recently added one more digit. The text claimed 29 digits, so adding another made the text incorrect. I fixed the text, and clarified that it's truncating, not rounding (though maybe we should prefer to round up?). Furthermore, I added the digit back, becaues I seem to remember my old fashioned tables of numbers format things in blocks of five digits aligned to the decimal point. I could be misremembering though. - lethe talk + 18:08, 7 April 2006 (UTC)
The page was moved a second time to ℮ (mathematical constant). I guess there is some support for the idea, but I'm sure also some opposition. I've moved back. - lethe talk + 20:31, 11 April 2006 (UTC)
I've protected the page from being moved. These semi-clever unicode-hacks are starting to become a bit tiring by now and it really shouldn't be moved without a discussion first. — Ruud 16:55, 12 April 2006 (UTC)
Isn't the curvature of e used in erecting structures? I remember learning that a parabolic shape wouldn't be as good as an e shape. Anyone have any information on this? 71.250.59.37 20:22, 3 May 2006 (UTC)
Not sure about others, but this sounds a bit odd to me - how can a number be both truncated and rounded? I would suggest "or" instead, or preferably replace with "correct to 20 decimal places"? Madmath789 13:16, 30 May 2006 (UTC)
Is there any good reason why the horizontal and vertical axes of the Image:E-ruud.png are not drawn to the same scale? Evercat 20:12, 9 June 2006 (UTC)
The text cites A005131 as the simple continued fraction of e, but OEIS:A003417 says it is. The latter looks more reasonable to me. Then the question is, what is OEIS:A005131? Lee S. Svoboda tɑk 22:11, 26 August 2006 (UTC)
I added a third generalized continued fraction that converges far more quickly than the first two. It corresponds to the series
1/1, 3/1, 19/7, 193/71, 2721/1001, ...
Each convergent adds 2-3 decimal digits of precision to its predcessor.
I also added a general formula for e^(2m/n) for |m|,n = 1,2,3,...; however, convergence slows as |m| increases in value. When m=1 and n=2 you get the formula for e.
Glenn L
The graph comparing f(x)=e^x to f'(x) is nice, but a little confusing, if only because x=.7 (whatever it is, don't have calculator handy), which gives f(x) = 2. Which is nice, but not entirely evident unless you know to look for it. Perhaps showing x=1 would help, and showing the equation "e^(.7whatever) = 2, which is the slope at that point, and e^1 = 1, which is the slope there." Perhaps even more explicitly labelling the slope of 2 would help (either with a direct label, or an old middleschool "rise over run" triangle, showing that it goes up 2 for every 1 over). And, I may be splitting hairs, but it seems like the line for e^x should be bolded, or that the f' line should not be given equal weight. I say this just because it is the first (and only) graph on the page, so it is doing double duty: showing the function e^x (very important) and showing that that derivative of e^x equals e^x (important, but less important than showing that function itself). Sir Isaac Lime 20:13, 19 September 2006 (UTC)
Reinstated my paragraph on APR (interest rates) after it was completely deleted by RandomP on the grounds that he didn't know what "percentage rate" meant. Expanded the text slightly to clarify, but a really detailed explanation of APR/interest probably belongs in an article on that subject. -- DarelRex 13:34, 26 September 2006 (UTC)
This is not a personal attack; please do not repeatedly delete my entire post on the grounds that it needs a tiny fix. I have now reposted it (again) with an extra sentence that hopefully alleviates the problem as best as I understand it from your above criticism. If further modification is necessary, please advise or revise instead of axing the whole thing again and again. Thanks. -- DarelRex 13:56, 26 September 2006 (UTC)
e is also relevant to measuring the difference between linear growth and exponential growth. If the doubling period for a process of exponential growth is estimated by linear approximation, the actual growth factor will be e after that time.
For example, assume that a bank continuously compounds interest, and we start with $1 in the bank, with current interest payments at a rate of $1/year. In order to calculate the annualised percentage rate, we might consider this rate to remain constant, and estimate the doubling period at a year — and thus, the annualised percentage rate at 100.
However, taking compound interest into account, we see that after a year, the account balance is $e, for an annualised percentage rate of approximately 172, much higher than our original estimate.
So if any "crazy" person might lift something out of context and use it to mispresent something else, then it has to be entirely removed? You are obviously determined to keep my paragraph out, so I will not repost it, even though I do not understand your criticisms. Your suggestion of what to replace my paragraph with will surely obfuscate its meaning to all but the most mathematically advanced readers. I give up; you win. -- 155.188.247.6 14:27, 26 September 2006 (UTC)
I think a lot of people would get more out of a "real world" example, such as e being involved in the difference between simple and compound interest, than all those very abstract equations. -- Hugh7 08:52, 24 January 2007 (UTC)
I think that a picture showing the tangent line at 1, instead of 2 would ilustrate the point much more clearly... a slope of one is easier to see. 160.39.168.58 04:25, 11 December 2006 (UTC)
Does that mean the additive identity is 0 and the multiplicative identity is 1, or does it mean "the [actions] of addition and multiplication and the numbers 0 and 1"? Could someone please clarify this on the page. -- Hugh7 08:44, 24 January 2007 (UTC)
If you do not know that zero is the additive identity and that one is the multiplicative identity, then this article is beyond your level. JRSpriggs 11:57, 24 January 2007 (UTC)
Right now it's listed as the sum of (1/n!) from 0 to infinity; this doesn't seem to be right because 1/0! is 1, or am I mistaken? (I had learned before that 0! is a special case equal to 1) Since 1/0! + 1/1! is already 2, the next few numbers (2 through 6, I think) make the value pass 1... could somebody clear this up for me? Robinson0120 02:04, 28 January 2007 (UTC)
Ruud's graph showing the tangent to e^x at x=0 was replaced by a nice SVG graph with a tangent drawn at a different place, and the simple definition that e is the unique number such that the slope of the tangent to e^x at 0 is 1 was replaced by the much more scary-sounding (equivalent but over-specified) definition that e is the unique number such that the slope of the tangent to e^x is e^x for all x. Why? Can we modify the SVG and the definition back to the much simpler version, such that the graph actually illustrates the condition? We could also draw some light curves for 2^x and 4^x just to illustrate that they have different slope, not 1, at x=0. Dicklyon 03:17, 28 January 2007 (UTC)
Dicklyon decided to revert rather than follow Wikipedia rules on reverting. Rather than give the editer the benefit of the doubt, he reverted rather than fix it. This is a violation of the revert policy. Please help if you can. —The preceding unsigned comment was added by 172.163.172.47 ( talk) 20:47, 4 February 2007 (UTC).
To EJ: I changed the indefinite integral for e to the definite integral form:
because it has a unique solution and it can be used to generate the series expression for e. You replaced it with:
which appears superficially to be a definite integral, but actually is ambiguous and equivalent to the indefinite integral form from which I was trying to get away. Nor is it simpler as you said it was. It includes an implied limit as the lower bound goes to negative infinity, which makes it more complex than my version. JRSpriggs 08:46, 6 February 2007 (UTC)
I asked EJ a similar question on his talk page yesterday, JR. Here's his response.
- Why is the integral improper? AFAICS, it is a usual convergent Lebesgue integral of a nonnegative function, there is no need to go through the limit .
- Anyway, I'm notoriously bad at estimating the level of mathematical sophistication needed for understanding particular problems, so if you think the original formula is easier, do not hesitate to revert. However, I should point out that the original formula also relies on a convention which might or might not be clear to less sophisticated readers, namely for negative x. -- EJ 15:22, 5 February 2007 (UTC)
While I have to concede his point (in a measure-theoretic sense, there are no improper integrals), I don't think the typical reader of Wikipedia is up to speed on the fine points that distinguish the many possible definitions of an "integral" from one another. So I'm reinstating JR's version of the formula, because I think it's better for our target audience. DavidCBryant 12:22, 6 February 2007 (UTC)
DavidCBryant, your rewrite of this section has at least three problems that I see: 1. You disconnected the reference to the math formula that is involved. You either need to refer to the History or Definition section above, or repeat the formula explicitly. 2. You introduced the informal imperative style "Think about an account...". Not good. 3. You dropped the connection to the illustration. Please work on it some more. Dicklyon 18:11, 6 February 2007 (UTC)
I know very little about mathmatical concepts such as this, so I don't feel very comfortable editing the article, but it's my understanding that e is an irrational number, and this doesn't come across very clearly in the article. Does anyone object to this being mentioned in the opening paragraph? I think it would help expalin why the number is not shown in its entirety. - R. fiend 18:44, 10 February 2007 (UTC)
User:Hypergeometric2F1(a,b,c,x) put in a formula back on 21 December 2005 that had previously been repeatedly inserted by a user who called it "Keller's Expression", presumably after himself. This self-promotion had been removed several times before. Today I removed it yet again. -- Dominus 16:33, 15 February 2007 (UTC)
Let us delete the section on mnemonics, "Remembering the digits of e". It adds nothing of value. JRSpriggs 11:18, 28 February 2007 (UTC)
I would disagree. wikipedia guidelines suggest space should be awarded based on interest and importance. remembering the digits of e both allows people to better remember e (which is important)and while it is hard to prove something interesting the methods based upon myself and my math class 100 of people were mildly (or more) interested in the methods for remembering particularly the Andrew Jackson portion Beckboyanch 08:30, 3 March 2007 (UTC)
Hi! Is there a way to calculate some incorrect but approximate value of e using some sort of finite fraction/series? (Like for PI, we have 22/7 or 355/311). If there is, I would really like to add it to the article.-- Scheibenzahl 20:23, 9 March 2007 (UTC)
The reason for the difference is that the (simple) continued fraction expression for π [3; 7, 15, 1, 292...] has no obvious pattern, while that for e [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1...] *does* have an obvious pattern. The best approximations for e involve truncation after terms 2, 5, 8, 11... yielding 3/1, 19/7, 193/71, 2721/1001... as described in my previous entry in this discussion. Glenn L 15:12, 27 May 2007 (UTC)