The Blackboard bold reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

# Blackboard bold

See the real Africa
Blackboard bold is a style of typeface often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical, or near-vertical lines) are doubled. The symbols usually describe sets of numbers and are also referred to as double struck, although attempting to produce them by double striking on a typewriter is unlikely to give satisfactory results. The symbols were first introduced by the group of mathematicans known as Nicolas Bourbaki.

In some texts, these symbols are simply shown in bold, and blackboard bold in fact originated from the attempt to write bold letters on blackboards in a way that clearly differentiated them from non-bold letters. Wikipedia too uses ordinary bold in place of blackboard bold, as browser support for the latter is far from universal.

TeX, the standard typesetting system for mathematical texts, does not contain direct support for blackboard bold symbols, but the add-on AMS Fonts package by the American Mathematical Society provides this facility; a blackboard bold R is written as `\\Bbb{R}` in regular text and as `\\mathbb{R}` in math mode.

In Unicode, a few of the more common blackboard bold characters (C, H, N, P, Q, R and Z) are encoded in the Basic Multilingual Plane (BMP). The rest, however, are encoded outside the BMP, from `U+1D538` to `U+1D550` (uppercase, excluding those encoded in the BMP), `U+1D552` to `U+1D56B` (lowercase) and `U+1D7D8` to `U+1D7E1` (digits). Being outside the BMP, these are very new and not widely supported.

The following table shows some of the more common uses of blackboard bold. The first column shows the letter as rendered by Wikipedia's LaTeX markup system. The second column shows the Unicode codepoint. The third column shows the symbol itself (which will only display correctly if your browser supports Unicode and has access to a suitable font). The fourth column describes typical usage in mathematical texts.

 `U+1D504` 𝔄 Represents affine space. Sometimes represents the algebraic numbers, the algebraic closure of Q (although a Q with an overline is often used instead). `U+2102` ℂ Represents the complex numbers. `U+1D507` 𝔇 Represents the unit disk in the complex plane. `U+1D509` 𝔉 field. Often used for finite fields, with a subscript to indicate the order. `U+210D` ℍ quaternions. (The H stands for William Rowan Hamilton>Hamilton.) `U+1D50D` 𝔍 Sometimes represents the irrational numbers, R\\Q. `U+1D50E` 𝔎 German word körper, which is German mathematical jargon for field. `U+2115` ℕ Represents the natural numbers. May or may not include 0. `U+1D512` 𝔒 Represents the octonions. `U+2119` ℙ Represents projective space, the probability of an event, or the prime numbers. `U+211A` ℚ Represents the rational numbers. (The Q stands for quotient.) `U+211D` ℝ Represents the real numbers. `U+1D516` 𝔖 Represents the sedenions. `U+1D517` 𝔗 Represents a torus. `U+2124` ℤ integers. (The Z is for Zahlen, which is German language>German for "numbers".)

Note that PNZQ ⊆ (AR) ⊆ RCHOS, and QAC.