arguing over one sentence isnt a productive. its amazing that in a place where everything is words and nothing is action, there is still a distinction between words and action; action is merging or rewriting articles that ppl have been talking about doing for months on the talk page.
below is what happens when a non-math major argues about math -- an extensive argument over whether e is more important than 2. its truly amazing how good the arguments are. but math is not social science. no matter how good you are at sophism, it does not change the truth.
I'm almost certain that all mathematicians would agree that e is more important than 3 in mathematics. Perhaps ''e'' is not more important than 3 ''in general'' (ie Christianity), but we're talking mathematics here.
the most important numbers in math are 1, 0, pi, i, e, and possibly -1. the probably best to take this on faith because even if you win the argument, you dont really win. maybe its because theyre used most often and are most singular (ie therere quite a few integers, but only one e -- this is a sophist slipery slope argument btw).
unfortunately the whole thing ended up undercutting someones RfA, delaying their chances for sysop.
From Talk:E (mathematical constant)#Important_numbers:
Important numbers
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)
The rest of the post...
- It is among the most important because it appears in extremely many places. Perhaps a better word would be fundamental. But special makes no sense. - Fredrik | talk 10:46, 11 November 2005 (UTC)
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- After a bit of research, I found out what the technical term for "weird" numbers like pi and e is... non-algebraic numbers. So that's in there now. Matt Yeager 21:54, 11 November 2005 (UTC)
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- That is not correct. Non-algebraic numbers are called transcendental numbers. Further more this is just one property of π and e, they are also irrational numbers, non-integer numbers... The imaginary unit is algebraic. They may not be as important as 0 and 1 but much more important than any other integer, which is just a sum of 1's. --R.Koot 00:13, 12 November 2005 (UTC)
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- If e is transcendental, why not put that in the article like it is for π?
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- Well, I dunno about "algebraic/non-algebraic", I'm no expert mathematician... but what is the last part of your paragraph about? You really truly believe that i is more important than, say, 2? REALLY? Can I quote you on that?
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- REALLY?
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- I'm lost for words.
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- Actually, whether or not i is more important is irrelevant. Whether e is, now that's relevant. And I can't imagine many people agreeing with you on this. (And by the way, I don't think any of your other terms apply, because I doubt that e is as important as, say, the sq. root of 2, which is also an irrational, non-integer number.) Matt Yeager 08:00, 13 November 2005 (UTC)
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- You may quote him on that, and many mathematicians would agree. i is more important than 2 because 2 is just the sum of 1 with itself, whereas i is the fundamental unit required to define complex numbers. Complex numbers are one of the most important developments of mathematics.
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- e is among the most important constants in mathematics because:
- "it appears in myriad mathematical contexts involving limits and derivatives" (according to MathWorld, which considers it the most important constant second to π)
- it connects complex numbers with exponentiation and trigonometry, in Euler's formula
- it appears in solutions to many differential equations
- it appears in results from number theory
- it is used to define important special functions such as the Gamma function and error function
- I'm sure someone can think of more reasons. Fredrik | talk 11:25, 13 November 2005 (UTC)
- e is among the most important constants in mathematics because:
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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)
- Just take some undergraduate-level book on calculus and count the instances of all numbers used in it. If you sort that list descendently it would look something like this: 0, 1, e, π, i, 2, 3, 4, ... They are the numbers used most, or in other words the most important. In your 7/7 example you make the classic mistake of confusing notation and meaning. To expres π and e you need infinite sums of a function of 1, so they are not as trivial as integers. --R.Koot 23:34, 13 November 2005 (UTC)
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- Not being an expert mathematician, I can't defend my "classic mistake of confusing notation and meaning", so I must turn to your logic of the undergraduate calculus book...
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- Tsk tsk. The statement in question in the article does NOT say "Alongside the number π and the imaginary unit i, e is one of the most important numbers in calculus" (I surely wouldn't dispute that!); it says "Alongside the number π and the imaginary unit i, e is one of the most important numbers in mathematics."
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- Take some 1st grade book on arithmetic (which surely counts as mathematics!) and count the instances of all numbers used in it. I doubt you'll find any occurances of e, but you certainly will find a lot of occurances of 2. Are you going to suggest that calculus is more important (not more advanced, not more complex, but more important) than arithmetic?
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- If I'm not mistaken, you have made the classic mistake of confusing high-level mathematics and mathematics. Matt Yeager 00:01, 14 November 2005 (UTC)
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- Indeed, to make a statement about mathematics in general, you would need to count the occurences in all literature ever published. Because the amount of text on calculus, analysis, probability theory, applied mathematics, ... is far larger than texts on basic arithmetic a calculus book would be a representative sample. --R.Koot 00:12, 14 November 2005 (UTC)
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- Proof? (It's not just basic arithmetic, either--it's every part from the most basic math in kindergarten up to high school algebra and geometry, at least.) If none is forthcoming, I guess the statement gets deleted as an unsourced, POV piece of information. Matt Yeager 00:17, 14 November 2005 (UTC)
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- (Oh, and not to mention that none of those forms of mathematics you mentioned would even exist without arithmetic.) Matt Yeager 00:18, 14 November 2005 (UTC)
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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)
- I disagree with removing i from important numbers. I like it more the way it was before this change. I plan to move back. Oleg Alexandrov (talk) 06:49, 14 November 2005 (UTC)
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- I took it out again--the reason that "i" unfortunately has to be removed is because (as far as I know) "i" is not transcendental. As the version calling "e" one of the most important numbers in mathematics [4] is unsourced (or given a truly dubious source) at best and (more likely) untrue at worst, and the version calling "i" transcendental is false, as well (to the best of my knowledge), there unfortunately is no good alternative. Either "i" goes or the entire sentence does (which'd be quite a shame). Matt Yeager 23:26, 15 November 2005 (UTC)
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- Nobody said i is transendental, where did you get that from? Oleg Alexandrov (talk) 23:32, 15 November 2005 (UTC)
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- I think you missed what I was saying there. Because the article NEEDS to say that e is one of the most important transcendental numbers, OR to say nothing at all on e's importance (because the statement that it's one of the most important numbers is unsourced and untrue--see the above discussion), "i" can't be included--you can't say something along the lines of "Alongside pi, e is one of the most important transcendental numbers (oh yeah, and i is important too, though it's not transcendental)." Matt Yeager 23:41, 15 November 2005 (UTC)
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- Here is a reference for you: Ask Dr. Math FAQ: About Pi: "the five most important numbers in mathematics, 0, 1, e, pi, and i" (my emphasis). - Fredrik | tc 00:35, 16 November 2005 (UTC)
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- And a source that actually supports your argument finally emerges! However, your source gives no evidence whatsoever for his opinion. On the George W. Bush article, you wouldn't claim "Along with George Washington and Abraham Lincoln, George W. Bush is one of the best presidents ever" just because you found a quote by someone (even someone who totally knows his stuff on politics--say, Dick Cheney) that said as much. Why? Because the quality of a president is an OPINION. (You agree, true?) Please, please, explain why the importance of a number is any less of an opinion. (By the way, now that you've sourced your statement, you COULD just put in the statement, "is often considered to be one of the most important numbers," followed by the link, in the opening statement, and that'd be that.)
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- Oh yeah, and one last question (which hasn't been answered yet, at least not to my satisfaction). Unless you're dropping your claim that 2 is (relatively) unimportant because it's just 1+1, then why is e any more important, as it's just (1/(1-1)! + 1/1! + 1/(1+1)! + 1/(1+1+1)! etc.)?
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- If you can give good, complete answers to those two questions (the only two real objections left), I'll drop this whole thing. Alternately, do the whole "is considered to be" thing, and I'll likewise drop it (though I would like to see that last question answered).
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- (And a quick note on the poll below--that's an arbitrary way of prematurely ending discussion, thrown in without anything resembling "I suggest a poll--any objections?" posted here first, and I'm not going to recognize it. Sorry.) Matt Yeager 05:17, 16 November 2005 (UTC)
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- Saying that GWB is the best president is an opinion, it is a fact that e, π and i are among the most used numbers in mathematics.
- For the integers you need a finite sum, for e you need an infinite sum of numbers calculated with divisions and factorials. --R.Koot 12:36, 16 November 2005 (UTC)
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- A poll is a good way of ending an edit war, because it shows what the community wants. Obviously the person who knows he is going to lose such a poll would object to it, so you can't. Not recognizing the outcome would most likely be considered vandalism. Sorry. --R.Koot 12:41, 16 November 2005 (UTC)
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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.
- Don't forget 0, at least as important as those others, and having a profound effect on mathematics. -lethe talk 20:10, 16 November 2005 (UTC)
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.
- R.Koot: So what if it is a fact that e and company are among the most-used numbers in mathematics? http://dictionary.reference.com/search?q=important says nothing whatsoever about frequent use as a criterion for importance.
- I don't see (in this context) a way to explain important in a different way than most used? --R.Koot 21:43, 16 November 2005 (UTC)
- R.Koot: Hmmm... I guess I understand. Thanks!
- R.Koot: See Wikipedia:Survey guidelines, particularily number 2.
- Feel free to add other alternatives. --R.Koot 21:43, 16 November 2005 (UTC)
- Oleg: I'm assuming the three paragraphs flush against the left margin are all from you. ... Alright, you've clearly stated your case--thank you very much, by the way. However, the one point I have left still remains, and I think that it's a good enough reason to keep the offending sentence out. The opinions of some Wikipedians and one external link do not merit enough to call one number more important than the other. "Considered to be one of the most important numbers", sure, no objections whatsoever. But just plain "one of the most important numbers"? There simply is not enough backing to that claim.
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)
- Matt, your stance looks to me like NPOV pushed to the extreme. Maybe you can quitely drop it, no? Oleg Alexandrov (talk) 22:31, 16 November 2005 (UTC)
- As there now is some evidence supporting the claim, I considered it, but really, there's no excuse for the statement being there. I'm going to do what I earlier suggested that one of you guys do and slightly edit the statement. If you all approve, then great, we're done. If not, well, that'll suck. Matt Yeager 02:44, 17 November 2005 (UTC)
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- I disagree with removing or editing "one of the most important numbers ...". Matt, drop it, really. Oleg Alexandrov (talk) 02:47, 17 November 2005 (UTC)
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- Since the "importance" of e seems to be a controversial opinion, I think Wikipedia:Neutral point of view policy requires that we *include* quotes showing people's opinions, even if there is no evidence whatsoever for that opinion. I'm going to do that now. (Should I group those quotes into an "Importance" section, or call that section "Quotes" ?
- Unfortunately, I only have quotes from mathematicians saying e is the most important number (or at least one of the top 5). I look forward to seeing balancing quotes from people saying some other number is more important.
- If we said something like "most frequently used" rather than "important", that would be a fact we could objectively check -- although I suspect lots of numbers are frequently used because of historical accidents, even though they are not fundamentally important -- numbers such as "360", "5 280", "25.4", etc.
- --DavidCary 06:03, 17 November 2005 (UTC)
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- David, I can assure you that there is no controversy over the importance of e. Paul August ☎ 13:56, 17 November 2005 (UTC)
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- It's not a controversial opinion. It's just Matt Yeager against the world. -- Dominus 14:09, 17 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)
- I reverted the article to the version before the story of Matt & Co. started. Please, let us finish this discussion here and move on. There is nothing to argue about. Oleg Alexandrov (talk) 16:32, 17 November 2005 (UTC)
