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Differentials should not be italicised according to ISO standards $$ \int f\,dx \Rightarrow \int f\,\mathrm{d}x $$ But should these symbols be italicised?

  1. Continuous functions: $C(X,Y)$ vs $\mathrm C(X,Y)$
  2. Imaginary unit: $i$ vs $\mathrm i$
  3. Lp spaces: $L^p(\mu)$ vs $\mathrm L^p(\mu)$
  4. Subscripts: $C_c(X)$ vs $C_{\mathrm c}(X)$, $\lVert\cdot\rVert_u$ vs $\lVert\cdot\rVert_{\mathrm u}$
Henricus V.
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  • It does not directly concern $\LaTeX$, but it could be more suitable to [tex.SE]. – anderstood Nov 02 '16 at 22:58
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    Logically, they should not be, as these are all operators/constants/pieces of notation, not variables. However, in practice, I don't recall ever seeing them non-italicised (by the same token, I have hardly ever seen a non-italicised differential). Thanks for bringing that up! – tomasz Nov 02 '16 at 23:02
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    Mathematicians mostly don't care about what ISO says. Some use \mathrm for differentials, others don't. Both are understandable. (Though the \mathrm version is ugly.) – Daniel Fischer Nov 02 '16 at 23:03
  • I think it was Littlewood who wrote "It was said of Jordan's writing, that if he had 5 elements on the same footing, as a,b,c,d,e, they would appear as a, $b$, $c'_0$, $\Delta^*$, and $\prod^i_v$. " – DanielWainfleet Nov 03 '16 at 03:48

1 Answers1

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Language is determined by actual usage, not by "authorities" (who are generally viewed by linguists as describers, not prescribers). See, for example, What Is 'Correct' Language, from the Linguistic Society of America.

Technical language is no different in this regard from ordinary language.

From what I've seen, mathematicians, at least in the U.S., tend to use an italicized $d$ in a differential (and this can be seen in the house style in many mathematics journals), whereas engineers and physicists generally use a roman $\mathrm{d}$ (the latter in accordance with what ISO says is the standard).

As for the specific symbols you mentioned, I would look at common usage in the journals that you would like to publish in; also, take geography into account because there are regional differences in typography as well. One final remark: Use your own personal sense of esthetics too.

Mitchell Spector
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