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I am new to this site and couldn't find this question after a quick search but it may have been asked before.

This is possibly the most inconsequential issue one can have, but it has been bothering me for months.

When I finish a line of math (especially with the double $$), I often end with a period. I also usually use the \text command to distinguish the period from a decimal point.

My question is: is there any difference at all? I don't seriously think anyone would ever notice unless they looked at the TeX code, so this is more of a theoretical question.


Which one is "correct"?

$$|f(x)-(y)|<\epsilon\text{.}$$

or

$$|f(x)-(y)|<\epsilon.$$
share|improve this question
1  
Welcome to TeX.SX! You can highlight code in your post using back-ticks. For code-blocks indent them by four spaces or use the {} on the gui. – Andrew Feb 21 at 20:28
1  
I usually use \text for the punctuation at the end of a displayed equation because in the font I usually use the text punctuation is noticeably different from the math one. But if they are similar, you can omit \text. Instead of \text{.} you can also type \text., which is shorter. – User Feb 21 at 21:20
    
Note that there may be a clear visual difference: for example, if you are using Palatino as the text font and AMS Euler for mathematics. – Senex Feb 21 at 22:29
2  
Math has its own rules, and a period (or other punctuation) might have a particular meaning. I just omit such (even if the result, considering the display "part of the sentence" is ungrammatical). – vonbrand Feb 21 at 23:52
up vote 35 down vote accepted

Since you mention \text, you're using LaTeX or AMS-TeX. I'll assume LaTeX.

First of all, your formulas are incorrect because they have $$ (see Why is \[ ... \] preferable to $$ ... $$?). This settled, let's look at fontmath.ltx, where we find, for the common punctuation one can find at the end of a formula,

\DeclareMathSymbol{,}{\mathpunct}{letters}{"3B}
\DeclareMathSymbol{.}{\mathord}{letters}{"3A}
\DeclareMathSymbol{;}{\mathpunct}{operators}{"3B}

As you see, the comma and the period are taken from the math letters font; the semicolon, instead, comes from the main text font (upright).

So, yes, in principle there is a difference. With \text{.} you get the period from the font that was current when the formula started, so it will be from the italic font in the statement of a theorem (under normal settings) and the same for the comma.

On the other hand, an italic period is not easy to distinguish from an upright one. Here's a comparison, first the punctuation sign in text mode (upright or italic), then in math mode:

enter image description here

I'd use the math mode ones, particularly for the semicolon. With other fonts the differences might be bigger, but I'd always go for upright notwithstanding the context.

As Guho rightly observes in comments, with \text you also lose the kerning between the last symbol and the punctuation; try a formula my students so often forget :-(

\[
\dim\operatorname{im} f+\dim\ker f=\dim V.
\]

and

\[
\dim\operatorname{im} f+\dim\ker f=\dim V\text{.}
\]

Kerning differences

People might argue whether the first is better than the second ad infinitum, though. The kerning in the first case is the reason why Knuth decided to take the period and the comma from the math letters font.

In case you fear a period or comma can be ambiguously seen as part of the formula, use a thin space before it, like \,. I wouldn't use more this space, but it's personal preferences. Somebody likes to separate punctuation with a quad (I heartily disagree).


If you're using AMS-TeX, the situation is fully similar, because the math symbol setting is the same as in plain TeX, which has

\mathcode`\,="613B
\mathcode`\.="013A
\mathcode`\;="603B

which comes to the same choice of math fonts.

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2  
+1. Would you mind commenting on the loss of kerning when \text is used? For example V. vs. V\text{.}? Might be a relevant addition to your last paragraph and a good extension on this related question for inline math. – Guho Feb 21 at 21:10
    
\text is defined also in amstex. So, even if it is rare that someone uses amstex, the first sentence is not correct :) – User Feb 21 at 21:11
    
@User You're right! – egreg Feb 21 at 21:14
1  
@CarstenS That can't apply to math anyway, I'm with Knuth on this (The TeXbook, solution of exercise 18.9, page 321): “…these experts recommend ‘k := j − 1; A [0] := accum; end;’. The author heartily disagrees.” – egreg Feb 21 at 23:38
1  
@MassimoOrtolano That's Claudio's convention. ;-) We had a discussion on the GuIT forum about this and I showed several books, old and new, where punctuation was used. – egreg Feb 22 at 15:05

I agree with egreg in that I think the one that looks better is the upright font, but in certain cases one might need the textfont rather than the math font.

If you want it to do it automatically just do

\makeatletter
{\catcode`\.=\active\global\def.{\mathfinaldotaux}}
\AtBeginDocument{\mathcode`\.="8000 }
\newcommand*\mathfinaldotaux
  {\@ifnextchar\]{\mathfinaldot}{\@ifnextchar${\mathfinaldot}{\mathchar`\.}}}
\newcommand*\mathfinaldot{\textnormal{.}}
\makeatother

This makes . active only in math mode, and and defines it to check if the next token is \] or $ (you could also check for \) but I don't think it's necessary) and in that case outputs \mathfinaldot, otherwise outputs a normal ..

You can do this same approach with ,, ;, etc. If you want we could create a macro to ease the definition:

\providecommand*\csdef[1]{\expandafter\def\csname#1\endcsname}
\makeatletter
\newcommand*\definemathfinal[2]
 {\begingroup\lccode`\~=`#1\lowercase{\endgroup
    \def~}{\csname mathfinal#1aux\endcsname}
  \AtBeginDocument{\mathcode`#1="8000 }
  \csdef{mathfinal#1aux}{\@ifnextchar\]{#2}{\@ifnextchar${#2}{\mathchar`#1}}}}
\makeatother
\definemathfinal{.}{\textnormal{.}}
\definemathfinal{,}{\,\textnormal{,}} % <- You can define easily with some personal
\definemathfinal{;}{\,\textnormal{;}} % <- preferences like spacing

This way you don't have to change your document at all, and it's easily configurable.

share|improve this answer
2  
What about \end{equation}, \end{align} and so on? – egreg Feb 21 at 22:02
1  
Not completely foolproof, true, but adding a checking for \end is “easy” (I thought about it but just wrote that code without actually checking if it compiles, so I decided to leave \end out :); altough it doesn't work with environments that grab the environment as an argument (that would require more work). For everything else, \mathfinaldot. – Manuel Feb 21 at 22:05

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