# How to best typeset “special” constants (complex unit i, Euler's number e,…)?

I'm trying to come up with a typographically appealing way to express "special" numbers such as the complex unit i = sqrt(-1) or Euler's number e. It has to be such that it cannot be confused with regular numbers (such as the running index i, for example), and would ideally work for serif as well as sans-serif fonts.

I was briefly thinking of typesetting these numbers in bold, but found that bold face is often used to indicate vector quantities.

[Edit: Johannes Küster suggests to use upright for constants (about 14 minutes into his talk.]

I've seen double-stroked small letters too, and must say this isn't without appeal. I have no idea how to consistently typeset those, though. The (outdated?) bbm package seems to provide at least some basic functionality.

What do you use to represent special numbers, why do use it, and how to you typeset your solution?

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Whatever you choose, you should be consistent about it and therefore create a macro for their presentation (see Consistent typography). For example, \newcommand{\complex}{\mathbbm{i}}. There should be no need for \ensuremath, since you'll most likely use these "mathematical elements" inside math mode anyway/mostly. –  Werner May 31 '12 at 22:45
Related question: Upright Lowercase \pi –  Peter Grill May 31 '12 at 23:04
I've seen tons of math books where those "special" numbers don't get any special treatment at all: just italics. I'd be adamant about excluding double stroked fonts. –  egreg May 31 '12 at 23:08
@Caramdir If you feel that confusion can arise, don't use i for indexing. My experience tells me that usually there's no harm in using i for both meanings. –  egreg May 31 '12 at 23:15

Unicode has special glyphs for these symbols: 0x2148 for imaginary i, 0x2149 for imaginary j, 0x2107 for Euler's constant, etc (although on most fonts they look ugly).

If you are using a unicode aware engine and a opentype math font, you can just type these directly or use the corresponding macro for them (ConTeXt uses \imaginaryi, \imaginaryj, \Eulerconst, etc.; I don't know what names unicode-math package for LaTeX uses).

EDIT: I don't know whether \Eulerconst refers to "Euler's number" e or not. As pointed out by Caramdir, it not used frequently.

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unicode-math defines them as \mitBbbe, \mitBbbi and \mitBbbj. You can see them with texdoc unimath-symbols, listed under “Ordinary symbols”. Note that the Euler constant (\Eulerconst in unicode-math) is not the same as the Euler's number (=natural exponent exp(1)). –  Caramdir Jun 1 '12 at 4:15
Actually, I have never seen (ℇ U+2107) used anywhere; and Wikipedia seems to be confused about what it stands for. So better to stick to e and γ. –  Caramdir Jun 1 '12 at 4:25
I looked into the Wikipedia and I don't know what 0x+2107 is supposed to represent. But it is strange that Unicode standard includes a separate slot for plank's constant, but not for Euler's number. The Unicode symbols for imaginary number, differential operator, probability, etc are not used too often because (a) until recently there were a few full unicode math fonts, and (b) their default implementations are ugly (though that is font dependent issue). I think that one should use the unicode input for these characters, the actual shape can be changed by patching the font on the fly. –  Aditya Jun 1 '12 at 7:34

Whenever I'm unsure about how I'll eventually want something to look, I'll create a \newcommand so that I can hope to control things globally.

In this particular case, I might define something like

\newcommand{\myspecial}[1]{\mathrm{#1}}


which could be used, for example, as

$\myspecial{e}$


(I wouldn't necessarily use \mathrm, it's just to demonstrate the idea).

Another reason I find this approach useful is that I can then easily grep the file to find all occurrences, something like

egrep 'myspecial' myfile.tex

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I'd even go further and define separate macros for all the constants, in case I want to change just one of them. –  Caramdir May 31 '12 at 23:04
@Caramdir good idea :) –  cmhughes May 31 '12 at 23:04

Just use roman (\mathrm) for all non-variables. In particular, this includes standard operators, functions, and constants (such as $\mathrm{lim, sup; exp, ln; e, i}$) and can be extended to any mathematical object that has a unique fixed meaning, without needing any parameters to be specified, throughout a particular work in which it is defined.

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Note that \mathrm{lim} is wrong with respect to spacing; use the predefined operator \lim (and the similar ones \sup, \exp and \ln). –  egreg Jun 3 '12 at 14:12
@egreg: Good point! I was only trying to compile a list of names. I'm new to this site and my attempt didn't work too well anyway. It seems that MathJax doesn't operate here. –  John Bentin Jun 4 '12 at 19:32
No, MathJax doesnt't work because we want to talk about (La)TeX code, so rendering it would not show the point! Welcome to TeX.SX! –  egreg Jun 4 '12 at 19:57

Consistency is the primary goal. So the first task is to know what "special numbers" we need and define commands for them:

\newcommand{\euler}{e}
\newcommand{\ramuno}{i}


(ramuno was how some Italian mathematicians of the 16th century called the quantity that squared gives –1; then Euler started using i).

The mathematical typography tradition usually didn't have a special treatment of these symbols. See, for example, n. 359 in Gauss's Disquisitiones Arithmeticae, where the equivalent of

$\cos\frac{\lambda kP}{e} + i\sin\frac{\lambda kP}{e}$


is found (the edition I consulted is from the Werke by the Königlichen Gesellshaft der Wissenschaften in Göttingen, vol. 1, 1863, page 450). There's no doubt what this i is denoting.

However, in recent times, under the influence of physics and applied mathematics, people started to denote "constants" with upright letters. There's even an ISO regulation about this, which is compulsory in some fields where uniformity among papers and books is very important.

In pure mathematics there's essentially no rule. Do as you like or how your field is used to. Using special names for the special numbers allow you to change the appearance of your document just by changing the definition.

If you feel that there may be confusion between the "imaginary unit" (no worse name could be chosen for it) and an index (for summations, for instance), you have three strategies:

1. use a special denotation for the imaginary unit;

2. don't use i as an index;

3. forget about it and let the reader know from the context.

Strategy 2 is used by Graham, Knuth and Patashnik in their "Discrete Mathematics". Strategy 3 is very common in math textbooks.

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