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Following the question "The \bar and \overline commands" which is simply about the lengths of both, I'd like to know when to use \bar and when to use \overline from a semantically viewpoint.

I always used \bar, because up until now I only had single letter mean values to type. But now I came to a problem where I needed a wider "bar".

Then I just tried

\documentclass{article}

\begin{document}
  \[ \bar{a} \overline{a} \]
  \[ \bar{abc} \overline{abc} \]
\end{document}

where one can see that they also differ in position (\overline is lower), and also in thickness (\overline is thicker).

So, the question here is:

What does \bar represent semantically? And when to choose it over \overline and vice versa?

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1  
For wider bars you can use my \widebar command (shameless plug). –  Hendrik Vogt Feb 13 '13 at 14:27
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3 Answers

up vote 11 down vote accepted

Semantically, don't use either. Use \conj, or \mean, or \variant or whatever the overline is meant to mean. Then in your preamble, do:

\newcommand*\conj[1]{\bar{#1}}
\newcommand*\mean[1]{\bar{#1}}

Then:

  1. Your document source becomes readable: you can determine the meaning right there and then.
  2. Your document becomes more flexible: if you decide to denote complex conjugation by a star instead you can simply redefine \conj without worrying about changing what \mean does.
  3. You can change from \bar to \overline on a whim and don't have to make that crucial decision now.
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5  
while the suggestion to use a "meaningful" command is excellent, the expansion would have to be more complicated to allow for single or multiple-letter arguments. since the original question mentioned both, that should be addressed in your answer. –  barbara beeton Feb 13 '13 at 22:22
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\bar{a} can mean just "another thing" like if you used a' or \tilde{a} or \diamondclub. You never use \overline for this.

However, if you denote an operation like complex conjugation, reversal, set closure or whatever, you can use whichever you want. You found out that somehow (to some people) \bar{a} seems "too subtile" for this purpose, and you can use the reasonable solution proposed in the other question. This goes along the fact that in this case, things like \overline{x+y}, \overline{2U+V}, \overline{a_1a_2 dots a_n} have their meaning as well.

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I have indeed observed a difference between {\overline} and {\bar}: Having 3 lines of formula in one {\align} environment, using overline in combination with a 3rd power like this:

\overline{b}^3

causes the 3rd equation to need more vertical space und the 3rd equation was shifted down a bit, which looked quite disturbing. Using

\bar{b}^3

solved the Problem, so all three equations have the same vertical distance now.

The following code produces a little sheet of pdf which illustrates some differences between bar and overline:

\documentclass{standalone}
\usepackage{amsmath}
\begin{document}
$\begin{array}{r}
a+b+c\\
a+b^3+c\\
a+\overline{b}+c\\
a+\overline{b}^3+c\\
a+\bar{b}+c\\
a+\bar{b}^3+c\\
a+\overline{b^3}+c\\
a+\bar{b^3}+c\\
a+b+c
\end{array}$
\end{document}

Note the different distances of equations and the different kommutation behavior of the {\bar} and {\overline} commands with the power command.

Finally i recommend always using {\bar} for single numbers in example. For complex conjugation of many numbers {\overline} of course is the appropiate choice.

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