A letter of the alphabet drawn with doubled vertical strokes is called doublestruck, or sometimes blackboard bold (because doublestruck characters provide a means of indicating bold font weight when writing on a blackboard). For example, , , , , , .... Important sets in mathematics are commonly denoted using doublestruck characters, e.g., C for the set of complex numbers, Q for the rational numbers, R for the real numbers, for Euclidean n-space, and Z for the integers.
The use of doublestruck characters is a relatively recent typesetting convention, with older book and manuscripts using either an unadorned capital letter (e.g., and in Peressini et al. 1998, pp. 1 and 5) or a bold capital letter (e.g., , , and in O'Neill 1966, pp. 3-5).
Doublestruck characters can be encoded using the AMSFonts extended fonts for LaTeX using the syntax \mathbbC, and typed in the Wolfram Language using the syntax \[DoubleStruckCapitalC], where C denotes any letter.
Many classes of sets are denoted using doublestruck characters. The table below gives symbols for some common sets in mathematics.
symbol | set |
algebraics | |
Booleans | |
-ball | |
complex numbers | |
-dimensional complex projective space | |
-disk | |
-dimensional Euclidean space | |
any field | |
Gaussian integer | |
quaternions, upper half-plane | |
hyperbolic plane | |
integers | |
identity matrix | |
natural numbers | |
octonions | |
primes | |
-dimensional real projective space | |
rational numbers | |
reals | |
real numbers in dimensions | |
real matrices | |
-dimensional real projective space | |
-sphere | |
-torus | |
integers | |
integers (mod ) | |
negative integers | |
positive integers | |
nonnegative integers |