Talk:E (mathematical constant)

ISO 80000-2

Due to ISO 80000-2 the operator "e" should be typed upright, not in italics. <spane class="autosigned">— Preceding unsigned comment added by 131.188.134.245 (talk • contribs)

Virtually no reliable sources have paid attention to the dictates of the ISO on this. Sławomir Biały (talk) 14:18, 2 August 2016 (UTC)

ISO does not dictate - it facilitates. On matters of style, WP is not required to follow reliable sources, though it often does. I see no reason myself not to follow ISO on this. Dondervogel 2 (talk) 09:31, 10 September 2016 (UTC)

Just by curiosity, I checked randomly in 10 maths books of my library. All 10 type the operator "e" slanted, and not upright (by the way, the operators are never in italics in books or articles, they are typed in a slanted font, which is not the same as italics). Personally, I always type the operator e as a letter symbol in a formula when I use TeX (which makes it slanted), and all the mathematicians I know do the same. I don't think ISO helps at all in these matters: it is too often totally disconnected with the reality of scientific publications. Sapphorain (talk) 10:38, 10 September 2016 (UTC)

Wikipedia is required to follow reliable sources. See WP:WEIGHT. In this case, following the ISO would give the views of a tiny minority undue weight, when the rest of the world uses the conventions adopted in this article. Also, per WP:MSM#Roman versus italic: "For single-letter variables and operators such as the differential, imaginary unit, and Euler's number, Wikipedia articles usually use an italic font." Sławomir
Biały 12:47, 10 September 2016 (UTC)

Not on matters of style. Also, i and e are neither variables nor operators - they are mathematical constants, which is precisely why they should be upright. Dondervogel 2 (talk) 13:31, 10 September 2016 (UTC)

Euler's number, the subject of this article, is explicitly mentioned in the guideline. Also, it's just false that we don't follow reliable sources in matters of style. We do follow reliable sources, precisely for the reason that not following those sources would be assigning WP:UNDUE weight to minority views. In this case, on the matter of how "e" is usually typeset. Sławomir Biały (talk) 13:40, 10 September 2016 (UTC)

The rule is about single-letter variables and operators. The imaginary unit and Euler's number are just examples, and they are also incorrect examples. As stated, the rule does not apply to mathematical constants and therefore applies to neither e nor i. Dondervogel 2 (talk) 22:25, 10 September 2016 (UTC)

Nope, wrong. It explicitly is about italicization if e and i. This came out of precisely this sort of perennial discussion. There was very strong consensus against this proposal when you made it at WT:MSM. This apparent denial of the consensus (and black-letter word of the guideline) appears to be tendentious. I consider this discussion closed. The matter was already settled more than a year ago. The appropriate avenue to lobby for change is now an RfC, not to make an end-run around past consensus in this strange way. Sławomir Biały (talk) 00:44, 11 September 2016 (UTC)

The fact is that mathematical constants are usually typed with a slanted font - as are also all unspecified constants in mathematical formulae. This is easy to check by browsing randomly on math books and papers. It is not the role of wikipedia contributors to decide how mathematical texts should be printed, and certainly not to adopt a style which is used almost nowhere else. Sapphorain (talk) 15:33, 10 September 2016 (UTC)

The purpose of WP's style guide is "to make using Wikipedia easier and more intuitive by promoting clarity and cohesion, while helping editors write articles with consistent and precise language, layout, and formatting". In other words it really is the role of WP contributors to decide how mathematical texts should be appear in Wikipedia. The criteria are clarity and cohesion, both of which would be well served by use of an upright e if this were followed uniformly throughout the project. Reliable sources are not relevant here unless they promote clarity. Dondervogel 2 (talk) 22:37, 10 September 2016 (UTC)

Let me add my voice to the consensus that the ISO does not determine usage on WP, the ISO standard is non-standard, and we shouldn't adopt it. --JBL (talk) 23:17, 10 September 2016 (UTC)

Right. I agree that we're not constrained per se by "sources" on matters of style, but we should generally follow the style used in the mathematical community. What style is used in the community for the number e couldn't be clearer-cut. ISO is often useful, but in this case they screwed up big time. It's an idiotic recommendation, and we should not only not follow it, but we should make it clear that we're deliberately rejecting it because it's nonsense. --Trovatore (talk) 23:37, 10 September 2016 (UTC)

To point out the obvious: adopting a guideline that nobody uses promotes neither clarity nor cohesion. It would be much better to use an italic e throughout the project. Would that be an acceptable compromise, in the name of clarity and cohesion? Sławomir Biały (talk) 00:36, 11 September 2016 (UTC)

I agree the MOS trumps ISO. That is its purpose. It would help clarity and cohesion if you were to listen to my argument for why e and i are out of scope of that particular guideline, because that guideline contradicts itself. If I were to say "All traffic lights are green except the red ones" would you conclude that amber lights were green? I think it is more likely that you would (rightly) ignore the statement because of the self-contradiction. To answer your question directly: if the mos made a clear (ie, non-contradictory) ruling on italicization of mathematical constants, based on consensus, it would help clarity and cohesion to implement that statement project wide. Dondervogel 2 (talk) 08:23, 11 September 2016 (UTC)

The last paper I wrote with a typewriter was in 1987 or 88. Since the 1990s mathematical journal are only accepting manuscripts typed with some brand of TeX. Most of them now even specify in which brand you should submit. And wikipedia also does use a TeX variant. As a result, in all mathematical papers and books (and in wikipedia) all isolated roman letter symbols one types in a formula will invariably appear slanted, whatever they represent. Unless of course one takes the trouble of typing {\rm… }, which nobody does (if an author did such an implausible thing it would most likely be suppressed at copy-proof). If ISO's recommendations, or anyone's recommendations, are not compatible with this simple observation, then they are disconnected from the real world, do not belong to a reliable source, and should not be invoked. In fact nothing at all needs to be invoked in this particular matter. As we don't need any "source" informing us that an apple is a fruit, we don't need any "manual of style" instructing us how to type mathematical constants. Sapphorain (talk) 11:07, 11 September 2016 (UTC)

I do not accept that it is implausible that an author might use correct italicization of variables (italics) and constants (upright). It is my experience that journal copy editors treat all single letter symbols as if they are variables (except unit symbols), which leads to many characters incorrectly appearing in italics. When I point out this error at proof stage, they are in nearly all cases willing to correct it. Dondervogel 2 (talk) 18:30, 11 September 2016 (UTC)

It is your opinion that this is an error. That opinion is not shared by the rest of the world, notably Wikipedia. Sławomir Biały (talk) 18:53, 11 September 2016 (UTC)

That the use of italics for a mathematical constant is in my opinion an error is one thing we can agree on. That the WP guideline is self-contradictory is not an opinion, but a demonstrable fact. Dondervogel 2 (talk) 19:34, 11 September 2016 (UTC)

Yes, you already pointed that. But as also already mentioned, the WP guideline is not needed, and not called for in that matter. The TeX version of WP will type your math formulae correctly - that is, as the majority of professional mathematicians do. Just use <math>... </math>, and save your time and energy by not leading a rearguard action. Sapphorain (talk) 20:09, 11 September 2016 (UTC)

It is not self-contradictory. Since, however, the plain English written there seems to be too difficult for certain editors to parse, I have gone ahead and improved the wording to reflect the established consensus in this matter. I therefore assume that this matter is completely satisfactorily resolved. Sławomir Biały (talk) 20:25, 11 September 2016 (UTC)

Pronunciation

Could someone add a sentence on how to pronounce this constant ? — Preceding unsigned comment added by Lobianco (talk • contribs) 09:49, 6 November 2016 (UTC)

...It's the letter e. Wouldn't say it's that hard to pronounce. -- numbermaniac (talk) 07:36, 19 March 2017 (UTC)

One suspects that he means the pronunciation of "Euler" 71.84.210.136 (talk) 21:04, 20 May 2017 (UTC)

The graph of $y=\ln x$ is not magical

I don't really see this edit as an improvement. If a reader is already familiar with logarithms, then the base of the natural logarithm does not need further explication, and if a reader is not familiar with logarithms, then telling them in a confusing way that e is the x-coordinate of a point on that graph also does not seem very clarifying. The first paragraph does say (later) that this means that e is the unique number whose natural logarithm is one. Sławomir Biały (talk) 01:39, 24 November 2016 (UTC)

Please examine v:Calculus I#Natural logarithm and exponential function. It seems to me that the natural logarithm came first and the $e$ came a little later. Am I mistaken?--Samantha9798 (talk) 01:46, 24 November 2016 (UTC)

But what does this have to do with the graph of the function? We already say that e is the base of the natural logarithm. Saying that the point $(e,1)$ is a point on the curve $y=\ln x$ is just an obfuscated way of saying the same thing! Sławomir Biały (talk) 01:49, 24 November 2016 (UTC)

I admit that saying it was the point ($e$,1) was unwise. I did switch to ($x$,1), but you undid that as well. As a matter of pedagogy, it makes sense to me that the natural logarithm should be taught first. $e$ follows logically from the natural logarithm. The dates are 1618 for $e$ and 1619 for some notion of the natural logarithm. You are going to confuse student for ever and ever just because of a few years priority? This is an important matter of pedagogy. Which is easier to learn? Some number theory formula or a graph with a point on it?--Samantha9798 (talk) 02:01, 24 November 2016 (UTC)

You added my idea back into the first sentence in your words. I am comfortable with your wording. I like the new top diagram you added.--Samantha9798 (talk) 02:16, 24 November 2016 (UTC)

I doubt that Napier referred to e as the x-coordinate of a point on a curve in 1618 (or 1619). That requires a good source if we're going to say that. Sławomir Biały (talk) 12:18, 24 November 2016 (UTC)

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Requested move 17 August 2017

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Withdrawn. No such user (talk) 07:29, 18 August 2017 (UTC)

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E (mathematical constant) → e (number) – ...or perhaps e (constant). Phrase "(mathematical constant)" is unwieldy, and as far as I can tell this is the only article using it; disambiguator "(number)". is well-attested in e.g. Category:Integers. "(mathematical constant)" does not add anything particularly specific that "(number)" does not, and the article itself starts with The number e is... WP:NCDAB recommends that If there are several possible choices for parenthetical disambiguation, use the same disambiguating phrase already commonly used for other topics within the same class and context, if any. Otherwise, choose whichever is simpler. For example, use "(mythology)" rather than "(mythological figure)". No such user (talk) 09:45, 17 August 2017 (UTC)

e (number) is easily confused with e numbers. e (constant) might also refer to the elementary charge. Sławomir Biały (talk) 10:54, 17 August 2017 (UTC)

• Oppose per Sławomir Biały. That, and I'm familiar with the confusion that happens with the title "E (number)" as the creator of {{R from E number}}. (In fact, I think E (number) may need to be retargeted to E (disambiguation) as a {{R from incomplete disambiguation}}, but that can be a discussion for another day.) Steel1943 (talk) 14:06, 17 August 2017 (UTC)

• Oppose. Both other suggested possibilities have been there for over 10 years without seeming to be an issue. But I don't think that you can compare this to, for example, 42 (number). There, the "42" always means the same number, but the article with "(number)" is about the number itself, while any others just happen to include that number in some way. Here, the symbol e can apparently refer to different numbers, so something more specific would seem to be needed. --Deacon Vorbis (talk) 14:36, 17 August 2017 (UTC)
• oppose. Sławomir Biały put it well – both alternatives can easily be interpreted in other ways. The current name works well as most people would describe it as a mathematical constant, not in any other way, and not find it too unwieldy.--JohnBlackburne^words_deeds 15:40, 17 August 2017 (UTC)
• Oppose as per above Power~enwiki (talk) 22:58, 17 August 2017 (UTC)

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The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Circular Definition

This article begins with the definition:

"The number e is a mathematical constant that is the base of the natural logarithm: the unique number whose natural logarithm is equal to one."

And, referring to the article on the natural logarithm, we find:

"The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459."

These two definitions are circular, and, without the numerical approximation of e in the latter, could (save for the description of e as irrational and transcendental), could apply to the common logarithm, or any other base.

In other words, it really only describes without defining. It would perhaps be useful to resolve the circularity. — Preceding unsigned comment added by Radagasty (talk • contribs)

I'm not concerned. There are multiple definitions of both terms given in the opening paragraphs. The opening sentence at Natural logarithm uses a non-technical definition to be more descriptive to the lay reader. power~enwiki (π, ν) 04:13, 26 October 2017 (UTC

(edit conflict) Both articles give multiple, independent definitions that do not rely on each other. This should hopefully be clear here; two more definitions are given in the next two sentences, and there is further explanation in the body of the article. --Deacon Vorbis (talk) 04:16, 26 October 2017 (UTC)

There is no circularity in the definition given in this article. The natural logarithm is defined here independently of the number e as the indefinite integral of 1/x. Sławomir Biały (talk) 10:31, 26 October 2017 (UTC)

In any case, the first sentence of the article is not meant to be a formal definition, and it is a mistake to treat the first sentence as such. The first sentence is a general description of the topic for the intended reader. If we want to have a formal definition, it should be lower in the article, such as in the "Definitions" section of natural logarithm. — Carl (CBM · talk) 14:33, 20 November 2017 (UTC)

@CBM. "The first sentence is a general description of the topic for the intended reader.".  Sounds very reasonable.
So, instead of a first sentence with a link to an article with in its first sentence a link back to e,  I propose:
"The number e (2.718...) is closely connected with any exponential curve, just as $\pi$ (3.141...) with any circle and $\phi$ (1.618...) with any golden rectangle."   Together with the basic picture visualizing this connection: curve, asymptote, tangent, and vertical segments of length 1 (at the tangent point), e and 1/e . -- Hesselp (talk) 17:44, 20 November 2017 (UTC)

How e is related with every exponential process

Radagasty (26 October 2017) correctly states the circularity in the starting sentences of e (mathematical constant) and Natural logarithm. And three commentators correctly state that there are alternative characterizations later on.  As an alternative I propose to start the article with the following rewording of the well known story on continuous compounding (see section Compound interest):
"The number e (2,718...) shows up when exponential/organic growth (constant growth rates on equal time intervals)  is compared with lineair/anorganic growth (constant increments on equal time intervals) starting at the same moment with the same value and the same rate.  At the moment the lineair proces has doubled the start value, the exponential process reaches 2,718... = e times this value."   Visualized in a picture with: an exponential curve and asymptote (horizontal), a tangent, vertical line segments at the tangent point and at the point where lineair growth has doubled the start value, and "1", "2" and "e" .
   Support?     -- Hesselp (talk) 19:51, 19 November 2017 (UTC)

No. That's pretty incomprehensible. --Deacon Vorbis (talk) 20:15, 19 November 2017 (UTC)

No also. Very cryptic and not of any help. Sapphorain (talk) 20:55, 19 November 2017 (UTC)

Nope. Also, none of the definitions in the lead is circular. In particular, the natural logarithm is defined in the first paragraph of the lead independently of the subject of the article. Also, what you wrote is mathematically wrong. Sławomir Biały (talk) 01:15, 20 November 2017 (UTC)

Obviously not, it's incomprehensible. The current version, by contrast, is good. --JBL (talk) 02:44, 20 November 2017 (UTC)

No. The proposed change is mathematically wrong also, unless those "equal time intervals" are infinitesimally small. I prefer a simpler definition like "the area under the curve y=1/x is 1.0 in the range x=1 to e." ~Anachronist (talk) 05:53, 20 November 2017 (UTC)

@Anachronist. 1. Mathematically wrong? Please clarify this.  For an exponential process ('function' in mathematics) can be described by the condition:  $f(t_{1}+\Delta t)/f(t_{1})=f(t_{2}+\Delta t)/f(t_{2})$ for all $t_{1}$ and $t_{2}$, and for all finite $\Delta t$.   Yes?

2.  The visualizations of both the arbitrary-exponential-curve-with-arbitrary-tangent definition  and  the 1/x-curve-with-square-equals-the-sofa-shaped-region definition, show e as a line segment compared with a unit segment. In my opinion the first construction is more comprehensible and more general ('simpler') than the second. Which argument(s) do you have for choosing the second (with the not at all trivial process of equalizing the sofa-area to the square-area)? -- Hesselp (talk) 14:16, 20 November 2017 (UTC)

You seem confused. Exponential functions, like $f(t)=2^{t}$ are the subject of a different article. Sławomir Biały (talk) 16:39, 20 November 2017 (UTC)

Doesn't  'natural logarithm'  denotes a function as well?  What is the connection between your remark and my two questions to Anachronist? -- Hesselp (talk) 17:44, 20 November 2017 (UTC)