14

The Latex command \ldots is often used to denote "and so forth". For instance,

$$ \pi \approx 3.1415\ldots $$

When a sentence ends with an \ldots, one is faced with the conundrum of how to properly terminate it. The "cleanest" way would of course be to add a terminating "period", thus signaling the reader that this grammatical unit has now reached completion. For instance,

$$ \rm{\ we\ have \ } \pi \approx 3.1415\ldots. \rm{\ However,} $$

We now have four dots at the end of the sentence, which seems like an excessive amount. The alternative however leaves a lingering feeling of dissatisfaction as the sentence does not feel finished:

$$ \rm{\ we\ have \ } \pi \approx 3.1415\ldots \rm{\ However,} $$

What is the best practice in such situations? Is there a "norm" to handle such a case when preparing a manuscript for publication?

Klangen
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    To be pedantic, $\pi=3.1415\ldots$ whereas $\pi\approx 3.1415$. Boom, the problem goes away. – Mark Grant Jul 04 '18 at 13:42
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    More seriously, I would suggest rewording the sentence so that it doesn't end with ellipses. – Mark Grant Jul 04 '18 at 13:42
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    I think an English usage forum, like https://english.stackexchange.com, would be a better place to ask a question of this sort. – Seva Jul 04 '18 at 13:43
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    I use period after \ldots, but I assume others do it differently. I hope this question was meant as a poll, as there is not really an answer. There is not even an agreement about periods at the end of sentences that end in displays! – darij grinberg Jul 04 '18 at 13:48
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    Maybe the sentence would feel more balanced if you had $\pi$ dots at the end. – Will Sawin Jul 04 '18 at 14:59
  • I'm voting to close this question as off-topic because it should be on https://tex.stackexchange.com/ and not here – Dima Pasechnik Jul 04 '18 at 18:41
  • @DimaPasechnik, I don't see how this is related to tex.SE. – gvgramazio Jul 04 '18 at 18:57
  • @gvgramazio - in absence of a better forum for maths typesetting, tex.SE would do. – Dima Pasechnik Jul 04 '18 at 18:59
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    @DimaPasechnik, occasionally, on tex.SE also minor things about typography are answered but generally question exclusively regarding typography is considered off-topic. Several proposals of typography.SE have to be done on area51 but none of them was successful. General questions about typography are currently answered on graphicdesign.SE. However, I think that this question could be answered on english.SE. – gvgramazio Jul 04 '18 at 19:33
  • @DimaPasechnik, also, from what I've understood from answers and comments, this question is highly language dependent. American English and UK English have different rules (and I suppose that also other English languages have different rules). This reason alone should be enough to move it to english.SE. – gvgramazio Jul 04 '18 at 19:42
  • @gvgramazio I would not be surprised if in english.SE hardly anyone knew what \ldots means. As well, while an example given in the question is English, it's not clear whether the question is about English, specifically... – Dima Pasechnik Jul 04 '18 at 20:18
  • @DimaPasechnik, Well, if it's not about English but in general is clearly too broad. e.g. In my language, Italian, the answer will be that no end dot is needed after horizontal ellipsis (\ldots is converted to U+2026 in this context). – gvgramazio Jul 04 '18 at 20:34

3 Answers3

18

I believe papers in English should be written in full and correct English sentences, with any mathematical formula being part of a sentence. Therefore, I believe that the correct form in this case would be

we have $\pi=3.1415\ldots\;$. However,

-- not

we have $\pi=3.1415\ldots$ However,

(and not

we have $\pi \approx 3.1415\ldots\;$. However,

).

(I inserted an instance of \; after \ldots, trying to improve the spacing.)

Iosif Pinelis
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    At least in spanish, the \ldots close the sentence, and there is no need of another period. – efs Jul 04 '18 at 13:48
  • @EFinat-S : Sorry, I don't know Spanish. – Iosif Pinelis Jul 04 '18 at 13:50
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    I agree with this answer. A related post about punctuation near math formulas is https://mathoverflow.net/questions/6675/periods-and-commas-in-mathematical-writing. – KConrad Jul 04 '18 at 13:52
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    @KConrad : Thank you for your comment. I see that the most upvoted answer at the link you supplied offers a similar thought: "when one writes a mathematical text one is writing sentences, to which all rules which apply to sentences of course apply." – Iosif Pinelis Jul 04 '18 at 14:16
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    Perhaps you should mention explicitly what you did, viz. to separate the three dots from the fourth dot by a thin space. – Emil Jeřábek Jul 04 '18 at 14:22
  • @EmilJeřábek : Thank you for your comment. I did think about mentioning this spacing adjustment, but then probably forgot to do that; it is now done, anyway. – Iosif Pinelis Jul 04 '18 at 14:42
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    Looking at this, it would appear that dots indicating some sort of abbreviation do replace the normal period at the end of a sentence in full and correct English sentences. Why is that different if a number is what's being abbreviated? (Honest question, as I'm not a native speaker.) – Baum mit Augen Jul 04 '18 at 15:14
  • @BaummitAugen : I think there is a difference between what is considered at that link and our situation. There at the link, we would have two periods in a row: "etc..", which just looks unaesthetic; cf. the recommendation of "etc.," at the same link. In our case, the single three-dot character produced by \ldots (which is just part of math formula) is followed by a period. – Iosif Pinelis Jul 04 '18 at 15:44
  • @BaummitAugen : Concerning the applicability of the rules, please see my comment to Carlo Beenakker's answer: "I think that in our case these guidelines for British and American English do not necessarily apply, because \ldots is part of a math formula, and not an ellipsis between words in a sentence". – Iosif Pinelis Jul 04 '18 at 15:51
  • But both the \ldots character and the ellipses character are displayed as three dots indicating some sort of omission, so I would have expected I'm supposed to apply the same rules. I would not have expected the fact it is part of some math to matter, as that seems like the opposite of treating the math as normal English. – Baum mit Augen Jul 04 '18 at 15:59
  • Although given there is no ISO standard for English, "a native speaker said so" is probably the most definite answer one can expect. – Baum mit Augen Jul 04 '18 at 16:06
  • @BaummitAugen I think only a committed prescriptivist would insist that there is a fact of the matter here. For what it's worth, I'm a native speaker/writer of American English and my own inclination would be to put a period after the $\ldots$, but at the same time I think the argument you pointed to also carries weight (and is the only argument I've seen so far which makes me waver in my own choice). – Todd Trimble Jul 04 '18 at 16:20
  • I'll dissent with this answer, and I will point to Allen Hatcher's dissenting answer in the link provided by @KConrad. To me, while there is a general and universal principle that mathematicians must follow logical rules with rigor, there is no such general and universal principle that writers must follow stylistic rules with rigor. Writing must be readable, and putting a period after an ellipsis makes it less readable. – Lee Mosher Jul 04 '18 at 18:01
  • @BaummitAugen : Agreeing that there is no ISO standard for written, technical English, there are published style manuals. The English Wikipedia gathers a few examples. And, relevant to the Question, placing the sentential punctuation following the equation's terminal expression's punctuation is consistent with Chicago, MLA, AP, and ETS. Of course, if writing for publication, the publication's style rules apply. – Eric Towers Jul 04 '18 at 18:35
  • @LeeMosher I disagree with your opinion that the period after the mathematical ellipsis makes it less readable. My experience is the opposite (there is a greater space between the final dot and the period than there is between the dots of the ellipsis, thus clearly indicating the distinct functions). – Todd Trimble Jul 04 '18 at 19:18
17

The principle mentioned by Iosif Pinelis that equations should follow the rules of grammar suggests to look at the OP in the broader context of the use of ellipsis in text: is $\ldots$ to be followed by a full stop period $.$ or not ?

The answer is "no" for British English (at least according to the University of Oxford Style Guide). For American English the answer is "yes" (at least for legal writing).

Carlo Beenakker
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  • A rule that equations should follow the rules of grammar does not imply a rule that the rules of grammar can override correct mathematical usage within/at the end of equations. In this case it's probably inconsequential to treat the ellipsis as both part of the equation and sentence termination, but in general there may be ambiguities introduced by this kind of practice, and I think the rule you cited should be interpreted as meaning "rephrase to avoid these cases". – R.. GitHub STOP HELPING ICE Jul 04 '18 at 15:19
  • Interesting. In contrast, the same Wikipedia article says this about American English: " If an ellipsis ends the sentence, then there are three dots, each separated by a space [emphasis mine -- I.P.], followed by the final punctuation". However, I think that in our case these guidelines for British and American English do not necessarily apply, because \ldots is part of a math formula, and not an ellipsis between words in a sentence, – Iosif Pinelis Jul 04 '18 at 15:22
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    @IosifPinelis But if we consider the math formula a part of a normal sentence, isn't the fact that the \ldots are set in math mode (as part of a math formula) a mere implementation detail? – Baum mit Augen Jul 04 '18 at 15:25
  • @BaummitAugen : I think this not a question of implementation or typesetting mode. Rather, I think the single three-dot character produced by \ldots is just part of math formula. – Iosif Pinelis Jul 04 '18 at 15:30
  • @IosifPinelis Thank you for your reply. However, I still do not see what exactly make the \ldots semantically different from "applicable to cats, dogs, …" (in which the '…' also appears as a single unicode character btw, in case that matters). – Baum mit Augen Jul 04 '18 at 15:34
  • @BaummitAugen : I think the semantic difference is that in our case the single three-dot character produced by \ldots is just part of math formula, whereas at your link the ellipsis is between words of a sentence or between different sentences. – Iosif Pinelis Jul 04 '18 at 15:57
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There are two possible correct answers.

  • The first one the the mathematician's: the ellipsis for some implied content thing that isn't written, while the full stop marks the end of a sentence. Since each of the two typographical signs has its own functions, both should be present. This is logically correct, but typographically wrong. :)

  • The second one is the typographer's, and it is better illustrated by the following three situations:

    1. Whenever a sentence contains an ellipsis right before the full stop, the full stop is no longer written.
    2. Whenever a sentence ends with an abbreviation (containing dots, such as "U.S.A." or "etc."), the full stop is no longer written (see also the links therein).
    3. Whenever a sentence ends with a quotation that itself ends with a full stop, the "outer" full stop is no longer written (it is a matter of debate, though, whether the remaining full stop should be inside or outside the quotation marks). Follow the links in the answers given here and see also this answer citing the Chicago Manual of Style.

To conclude, whenever a full stop would logically follow another typographical sign that itself ends with a dot, the full stop is no longer written (it "fuses" with the one preceding it).

Alex M.
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    Consider an excerpt from an imaginary text for math-phobic students, where removal of the period results in uncomfortable ambiguity. Choice 1: "The arclength $L$ subtended by the angle POQ is given by the formula $L=\pi RA/180$. Recall that $\pi$ is Ludolph’s constant, $3.14159\ldots$ . $R$ is the radial length, and $A$ is the measure of the angle POQ in degrees." Choice 2: "The arclength $L$ subtended by the angle POQ is given by the formula $L=\pi RA/180$. Recall that $\pi$ is Ludolph’s constant, $3.14159\ldots R$ is the radial length, and $A$ is the measure of the angle POQ in degrees." – Todd Trimble Jul 04 '18 at 21:13
  • The link you gave for item 1 confirms that Oxford prescribes the "no fourth dot" style. But scrolling up a little on the page, I see that this is not the unanimous decision of all styles. – Andreas Blass Jul 04 '18 at 22:11
  • I believe that the current "consensus" (if such exists - it's at least a trend) on periods at the end of quotations is predicated on whether or not the period belongs with the quoted sentence - (He said, "No, thank you.") vs (He spoke about "stuff".) – Sam Benner Jul 04 '18 at 22:22
  • @ToddTrimble: You are cheating :) because you ignore spacing. You use $3.14159 \ldots R$ instead of, at least, $3.14159 \ldots$ $R$, which would allow TeX to insert better spacing. Even better, you could manually force clearer spacing with appropriate LaTeX commands. Note that all the style and typographical conventions texts found in the links I provided insist on the importance of spacing even more than on the importance of punctuation. – Alex M. Jul 05 '18 at 09:13
  • I don't believe that any sentence about TeX starting with "Even better, you could manually force clearer spacing" is good advice. (If you know how to insert correct spacing, you will do so and don't need the advice. If you don't know how to insert correct spacing, then TeX will do a better job than you do, even if it's not perfect.) – LSpice Feb 20 '19 at 15:55