Letter with double stroke

This article is about markup. For the characters, see vertical double line .

Some of the basic sets of numbers are often denoted by double-dashed letters.

Letters with a double line are letters in which one or more lines of the letter - often a vertical one - are traced twice. This type of font is used in mathematics . There it occurs mainly in the standard names of the basic number ranges :

• ${\displaystyle \mathbb {N} }$for the natural ,
• ${\displaystyle \mathbb {Z} }$for the whole ,
• ${\displaystyle \mathbb {Q} }$for the rational ,
• ${\displaystyle \mathbb {R} }$for real ,
• ${\displaystyle \mathbb {C} }$for the complex numbers

use

The double line originally comes from the lecture on the blackboard , where it is used to mark letters that are shown in bold in the printed template , which can only be reproduced by handwriting by coloring in with great effort. Accordingly, this font is also called blackboard bold in English and has similar names in other languages. In the 1960s, letters with double bars found their way into printed texts, and the earliest work is probably a book on complex analysis by Robert Gunning and Hugo Rossi from 1965.

Some authors, such as Jean-Pierre Serre , continue to use ordinary bold letters in printed texts and dispense with the double bar at all, but letters with double bars are generally accepted as designations for the most important numbers. In addition, the usage in mathematical notation is inconsistent. In schools it is sometimes customary to mark all sets with a double line, for example for the domain and for the solution set . Outside of school, letters with a double bar are used much less often, mostly they are reserved for sets with a certain algebraic structure . The number sets of the hypercomplex numbers are often denoted by letters with double lines, for example for quaternions , for octonions and for sedenions . In addition to the Latin capital letters, other characters with a double bar are also used, so there is seldom a lower case i with a double bar (ⅈ) as an imaginary unit , the number 1 with a double bar (?) is used as a designation for the indicator function or for the identity matrix and that small Greek My with double dash for the group of roots of unity . ${\displaystyle \mathbb {D} }$ ${\displaystyle \mathbb {L} }$ ${\displaystyle \mathbb {H} }$ ${\displaystyle \mathbb {O} }$ ${\displaystyle \mathbb {S} }$

Coding

In LaTeX , the AMS font package provides amsfontsthe command \mathbbfor displaying letters with double bars. Other packages also provide commands - some under the same name - which can display other characters with double bars in addition to Latin capital letters.

In Unicode there were initially a few selected characters with double bars in the Unicode block of letter-like symbols . With version 3.1 the unicode block mathematical alphanumeric symbols was introduced, which contains the still missing Latin capital letters, all Latin lower case letters and all digits with double lines. In addition, since version 6.1 there is the Unicode block Arabic mathematical alphanumeric symbols with Arabic letters with double bars.

Individual evidence

1. ^ Robert C. Gunning, Hugo Rossi: Analytic functions of several complex variables. Prentice Hall 1965.
2. ↑ Willy Meersmann (Ed.): Mathematik-Lexikon. Cornelsen Scriptor, 1994. ISBN 3-589-20894-5 .
3. ↑ James Milne : Etale cohomology. Princeton University Press, 1980.
4. ↑ Scott Pakin: The Comprehensive LaTeX Symbol List. ( Memento from February 14, 2016 in the Internet Archive ) (PDF)

Web links

• Eric W. Weisstein : Doublestruck . In: MathWorld (English).