Should subscripts in math mode be upright?

Question

In one-letter subscripts, like $x_i$, the subscript is usually typeset italic.

Is this the typographically right thing to do? Consider this case:

The Boltzmann constant is often written as $k_B$, which is short for $k_{Boltzmann}$. But the lengthy Boltzmann looks strange if typeset all italic. So I usually write $k_{\mathrm{Boltzmann}}$.

But shouldn't then, for consistency, the B in $k_B$ also be upright? And how about the i in $x_i$?

Answer 1

Using "all italics" is unfortunately an often committed sin. You should italicize only variables.

Everything else should be upright. For example:

• function names (sin, cos, log, ln etc...)
• dimensionless numbers (Re, Pr, Ra...)
• exact infinitesimal increments (dx, dy et... in BOTH integrals and differentials)
• descriptive text
• all descriptive variable indices (unless they are also variables)

Exceptions to this rule may still apply, i.e. the Euler-number $e$ is no variable, but still traditionally written in italics.

Some of the above was stolen from the "Please Make A Note" blog. More detailed information can be found in "Typefaces" from NIST.

Answer 2

\text is not the right command to use, as its argument will be typeset in the current font, which may be italics.

\usepackage{amsmath} % for extended version of \textup
\newcommand*{\Boltzmann}{k_{\textup{B}}}

$\vec{F}_{\textup{in}}+\vec{F}_{\textup{out}}=\vec{0}$

What subscripts are to be set in upright font and what in italics is well explained by Boffin. (I disagree about the d for the differential, though, but that's another story: be consistent, that's all for this particular aspect.)

Answer 3

For me it depends on the context. Using your example, I would agree that you should use $k_{\text{B}}$ since it is short for $k_{\text{Boltzmann}}$. Note the use of \text{...} from the amsmath package, that does a decent job of sticking to the math mode font size, depending on the context.

On that note, $k_{Boltzmann}$ "looks strange" because (La)TeX typesets it like it does regular math, which in this case is the variable B, followed by the variable o, followed by the variable l, and so on. My use of the term "variable" may be incorrect. The point I'm trying to make is that each letter is treated on it's own in math mode, rather than combining them like is done in text mode. The spacing is correct as-is in math mode, it just doesn't look like text.

With this discussion in mind, I hope you agree that $x_i$ should remain $x_i$. Of course, if you are referring to i in your text somewhere (instead of $i$), then it should be upright. IMHO, it is all (mostly?) driven by context.

Answer 4

Based on egreg's answer and Henri Menke's comment, here's a comparison between amsmath's \text, \textup, and \textnormal commands. From the three, only \textnormal is immune from the outer text mode format, as the name says.

\documentclass{article}

\usepackage{amsmath} % for extended version of \textup

\begin{document}
\noindent
{\itshape\(\text{text}|\textup{up}|\textnormal{normal}\)}\newline
{\bfseries\(\text{text}|\textup{up}|\textnormal{normal}\)}\newline
\sffamily\(\text{text}|\textup{up}|\textnormal{normal}\)
\end{document}

Answer 5

Boffin's answer already provides the correct information. I just want to add to the discussion 'elementary charge' vs. 'Euler number' in the comments:

While physical constants (such as the elementary charge 'e', gravitational constant 'G', speed of light 'c', ...) are typeset italic, all mathematical constants (such as Euler number 'e', imaginary unit 'i', ...) should be typeset upright. This also provides a helpful distinction between, e.g., an index 'i' (italic) and the imaginary unit 'i' (upright).

All in all, the document by NIST which was already linked by @Boffin, provides a concise and complete summary.

Answer 6

This is matter of personal style. In my own documents, I follow similar rules: if subscript stands for people's name I type it using \text command (defined in amsmath package), e.g. $\varepsilon_\text{F}$ (the Fermi energy), $a_\text{B}$ (the Bohr radius), $r_\text{D}$ (Debye's radius), etc. Russian indexes are usially typed upright: $P_\text{т.и}$ (power of bremsstrahlung).