Blackboard bold

Blackboard bold is a style of typeface often used for certain symbols in mathematical and physics 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 are also nearly universal in their interpretation, unlike their normally-typeset counterparts, which are constantly reused.

Related Topics:
Typeface - Mathematical - Physics - Number - Typewriter

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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. Writing actual bold letters using chalk is simple when you turn the chalk sideways.

Related Topics:
Bold - Blackboard

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It is frequently claimed that the symbols were first introduced by the group of mathematicians known as Nicolas Bourbaki. There are several reasons to doubt this claim: (1) the symbols do not not appear in Bourbaki publications (rather, ordinary bold is used) at or near the era when they began to be used elsewhere, for instance, in typewritten lecture notes from Princeton University (achieved in some cases by

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overstriking R or C with I), and (an apparent first) typeset in

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Gunning and Rossi's textbook on several complex variables; (2) Jean-Pierre Serre, a member of the Bourbaki group, has publicly inveighed against the use of "blackboard bold" anywhere other than on a blackboard.

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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.

Related Topics:
TeX - American Mathematical Society

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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.

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The following table shows some of the more common uses of blackboard bold.

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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 typical usage in mathematical texts.

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Note that mathbb{P} subseteq mathbb{N} subseteq mathbb{Z} subseteq mathbb{Q} subseteq mathbb{R} subseteq mathbb{C} subseteq mathbb{H} subseteq mathbb{O} subseteq mathbb{S}.

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