Blackboard bold

To imitate a bold typeface on a typewriter, a character can be typed over itself (called double-striking);[1] symbols thus produced are called double-struck, and this name is sometimes adopted for blackboard bold symbols,[2] for instance in Unicode glyph names.

In typography, a typeface with characters that are not solid is called inline, handtooled, or open face.

[8][9] Blackboard bold originated from the attempt to write bold symbols on typewriters and blackboards that were legible but distinct, perhaps starting in the late 1950s in France, and then taking hold at the Princeton University mathematics department in the early 1960s.

or ZZ; at the blackboard, lecturers began writing bold symbols with certain doubled strokes.

Early examples include Robert Gunning and Hugo Rossi's Analytic Functions of Several Complex Variables (1965)[12][10] and Lynn Loomis and Shlomo Sternberg's Advanced Calculus (1968).

In 1979, Wiley recommended its authors avoid "double-backed shadow or outline letters, sometimes called blackboard bold", because they could not always be printed;[13] in 1982, Wiley refused to include blackboard bold characters in mathematical books because the type was difficult and expensive to obtain.

using the letters I and R with a negative space between;[15] in 1988 Robert Messer extended this to a full set of "poor person's blackboard bold" macros, overtyping each capital letter with carefully placed I characters or vertical lines.

[18] Unicode included the most common blackboard bold letters among the "Letterlike Symbols" in version 1.0 (1991), inherited from the Xerox Character Code Standard.

[20] The Chicago Manual of Style's recommendation has evolved over time: In 1993, for the 14th edition, it advised that "blackboard bold should be confined to the classroom" (13.14); In 2003, for the 15th edition, it stated that "open-faced (blackboard) symbols are reserved for familiar systems of numbers" (14.12).

[21] TeX, the standard typesetting system for mathematical texts, does not contain direct support for blackboard bold symbols, but the American Mathematical Society distributes the AMSFonts collection, loaded from the amssymb package, which includes a blackboard bold typeface for uppercase Latin letters accessed using \mathbb (e.g. \mathbb{R} produces

[23] 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.

In addition, a blackboard-bold μn (not found in Unicode or amsmath LaTeX) is sometimes used by number theorists and algebraic geometers to designate the group scheme of n-th roots of unity.

[27] Note: Only uppercase Roman letters are given LaTeX renderings because Wikipedia's implementation uses the AMSFonts blackboard bold typeface, which does not support other characters.