Symbols for the number sets

Mathematicians commonly use special lettering for the real numbers and other standard number sets. Traditionally these were typeset in bold. In the ordinary course of events, but mathematicians do not have access to bold chalk, so they invented special symbols that are now often used for the number sets. Such symbols are known as “blackboard bold” (or double-stroked) letters; in place of the heavier strokes of a bold font, (some) strokes of the letters are doubled. The minimum useful set is upper-case letters “I”, “N”, “R”, “Q” and “Z”; some fonts offer a figure “1” (for a unit matrix — not a number set at all).

A set of blackboard bold capitals is available in the AMS msbm fonts (msbm is available at a range of design sizes, with names such as msbm10). The AMS actually provides a pair of font families (the other is called msam), which offer a large number of mathematical symbols to supplement those provided in Knuth’s fonts. The fonts are available in Type 1 format in modern distributions. Support for using the fonts under LaTeX is available in packages amssymb and amsfonts. The font shape is a rather austere sans, which many people don’t like (though it captures the essence of quickly-chalked writing rather well).

The bbold family is set of blackboard bold fonts written in MetaFont. This set offers blackboard bold forms of lower-case letters; the font source directory also contains sources for a LaTeX package that enables use of the fonts. The fonts are not available in Type 1 format.

The bbm family claims to provide “blackboard” versions of most of the cm fonts … including the bold and bold-extended series. Again, the fonts are designed in MetaFont and are not available in Type 1 format. LaTeX macro support comes from a package by Torsten Hilbrich.

The doublestroke family comes in just roman and sans shapes, at a single weight, and is available both as MetaFont sources and as Type 1; the font covers the uppercase latin letters, lowercase “h” and “k”, and the digit “1”.

A document that shows the bbm, bbold, doublestroke and msbm fonts, so that you can get a feel for their appearance, is available (CTAN package blackboard).

The boondox font set consists of Type 1 versions of the STIX mathematics set (the originals are distributed in OTF format). The set contains a font “BOONDOXDoubleStruck-Regular” (blackboard bold) (as well as a “bold” version of that.

An alternative source of Type 1 fonts with blackboard bold characters may be found in the steadily increasing set of complete families, both commercial and free, that have been prepared for use with (La)TeX (see “choice of outline fonts”). Of the free sets, the txfonts and pxfonts families both come with replicas of msam and msbm, but (as noted elsewhere, there are other reasons not to use these fonts); revised versions of the fonts, newtx and newpx are better adjusted. The mathpazo family includes a “mathematically significant” choice of blackboard bold characters, and the fourier fonts contain blackboard bold upper-case letters, the digit “1”, and lower-case “k”.

The “lazy person’s” blackboard bold macros:

\newcommand{\R}{{\textsf{R}\hspace*{-0.9ex}%
  \rule{0.15ex}{1.5ex}\hspace*{0.9ex}}}
\newcommand{\N}{{\textsf{N}\hspace*{-1.0ex}%
  \rule{0.15ex}{1.3ex}\hspace*{1.0ex}}}
\newcommand{\Q}{{\textsf{Q}\hspace*{-1.1ex}%
  \rule{0.15ex}{1.5ex}\hspace*{1.1ex}}}
\newcommand{\C}{{\textsf{C}\hspace*{-0.9ex}%
  \rule{0.15ex}{1.3ex}\hspace*{0.9ex}}}

are almost acceptable at normal size if the surrounding text is cmr10 (the position of the vertical bar can be affected by the surrounding font). However, they are not part of a proper maths font, and do not work in sub- and superscripts. As we’ve seen, there are plenty of alternatives: that mythical “lazy” person can inevitably do better than the macros, or anything similar using capital “I” (which looks even worse!). Voluntary (La)TeX effort has redefined the meaning of laziness (in this respect!).

FAQ ID: Q-numbersets