# Blackboard bold

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Blackboard bold is a typeface style that is 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 denote number sets. Blackboard bold symbols are also referred to as double struck, although they cannot actually be produced by double striking on a typewriter.

In some texts these symbols are simply shown in bold: 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, and then made its way back in print form as a separate style from ordinary bold,[1] possibly starting with the original 1965 edition of Gunning and Rossi's textbook on complex analysis[2]. Some mathematicians, therefore, do not recognize blackboard bold as a separate style from bold: Jean-Pierre Serre, for example, has publicly inveighed against the use of "blackboard bold" anywhere other than on a blackboard, and uses double-struck letters when writing bold on the blackboard[3], whereas his published works consistently use ordinary bold for the same symbols[4]. It is sometimes erroneously claimed[1] that Bourbaki introduced the blackboard bold notation, but whereas individual members of the Bourbaki group may have popularized double-striking bold characters on the blackboard, their printed books use ordinary bold[5].

The symbols are nearly universal in their interpretation, unlike their normally-typeset counterparts, which are used for many different purposes.

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

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) in the Letterlike Symbols (2100–214F) area, named DOUBLE-STRUCK CAPITAL C etc. 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 relatively new and not widely supported.

## Contents

### Examples

The following table shows all available Unicode blackboard bold characters.

The first column shows the letter as typically rendered by the ubiquitous 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 known typical (but not universal) usage in mathematical texts.