 TOPICS  # Doublestruck

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 \mathbb C , 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

C, Q, R, Set, Z

## Explore with Wolfram|Alpha More things to try:

## References

Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 112 and 398, 1987.O'Neill, B. Elementary Differential Geometry. San Diego, CA: Academic Press, 1966.Peressini, A. L.; Sullivan, F. E.; and Uhl, J. J. Jr. The Mathematics of Nonlinear Programming. New York: Springer-Verlag, 1988.

Doublestruck

## Cite this as:

Weisstein, Eric W. "Doublestruck." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Doublestruck.html