 Blackboard bold

"Doublestrike" redirects here. For other uses, see Double Strike (disambiguation).
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 nearvertical 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 type: blackboard bold in fact originated from the attempt to write bold letters on blackboards in a way that clearly differentiated them from nonbold 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: JeanPierre Serre, for example, has publicly inveighed against the use of "blackboard bold" anywhere other than on a blackboard,^{[citation needed]} and uses doublestruck 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 doublestriking bold characters on the blackboard, their printed books use ordinary bold.^{[5]}
The symbols are nearly universal in their interpretation, unlike their normallytypeset 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 addon 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 DOUBLESTRUCK CAPITAL C etc. The rest, however, are encoded outside the BMP, from
U+1D538
toU+1D550
(uppercase, excluding those encoded in the BMP),U+1D552
toU+1D56B
(lowercase) andU+1D7D8
toU+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.
Unicode (Hex) Symbol Mathematics usage U+1D538
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