Editing Blackboard bold (section)

==History==
[[File:Blackboard_bold_in_typewritten_notes_from_Gunning_(1966).jpg|thumb|right|upright=1.25|Typewritten lecture notes by [[Robert C. Gunning|Gunning]] (1966), showing "blackboard bold" style '''R''' and '''C''' achieved by double-striking each letter with significant offset{{r|gunning}}]]
[[File:Blackboard_bold_in_typewritten_notes_from_Narasimhan_(1966).png|thumb|right|upright=1.25|Typewritten lecture notes by [[Raghavan Narasimhan|Narasimhan]] (1966), with "blackboard bold" style '''R''' and '''C''' achieved with an inline typewriter face{{r|narasimhan}}]]

Traditionally, various symbols were indicated by [[boldface]] in print but on blackboards and in [[manuscript (publishing)|manuscript]]s "by wavy underscoring, or enclosure in a circle, or even by wavy overscoring".{{r|manuscripts}}

Most typewriters have no dedicated bold characters at all. To produce a bold effect on a typewriter, a character can be ''double-struck'' with or without a small offset. By the mid 1960s, typewriter accessories such as the "Doublebold" could automatically double-strike every character while engaged.{{r|karch}} While this method makes a character bolder, and can effectively emphasize words or passages, in isolation a double-struck character is not always clearly different from its single-struck counterpart.{{r|webb|waite-arca}}

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.{{r|webb}}{{r|rudolph}} Mathematical authors began typing faux-bold letters by double-striking them with a significant offset or over-striking them with the letter ''I'', creating new symbols such as
<!-- Blackboard bold R, N, accomplished with over-struck I; bold C accomplished by 2 copies. Sorry for the mess of raw HTML: -->
<span style='font-size: 1.15em; font-family: Courier, "Courier New", "Lucida Typewriter", "Nimbus Mono L", "Liberation Mono", monospace; letter-spacing: -.25em; padding: 0 .28em 0 0;'>IR</span>,
<span style='font-size: 1.15em; font-family: Courier, "Courier New", "Lucida Typewriter", "Nimbus Mono L", "Liberation Mono", monospace; letter-spacing: -.22em; padding: 0 .2em 0 0;'>IN</span>,
<span style='font-size: 1.15em; font-family: Courier, "Courier New", "Lucida Typewriter", "Nimbus Mono L", "Liberation Mono", monospace; letter-spacing: -.4em; padding: 0 .4em 0 0;'>CC</span>,
or <span style='font-size: 1.15em; font-family: Courier, "Courier New", "Lucida Typewriter", "Nimbus Mono L", "Liberation Mono", monospace; letter-spacing: -.37em; padding: 0 .37em 0 0;'>ZZ</span>;
at the blackboard, lecturers began writing bold symbols with certain doubled strokes.{{r|webb}}{{r|rudolph}} The notation caught on: blackboard bold spread from classroom to classroom and is now used around the world.{{r|webb}}

[[File:Blackboard bold in print in Loomis and Sternberg (1968).jpg|thumb|upright=1.25|A page from [[Lynn Harold Loomis|Loomis]] & [[Shlomo Sternberg|Sternberg]] (1968), showing an early example of "blackboard bold" style '''R''' and '''C''' in a printed book{{r|loomis-sternberg}}]]
The style made its way into print starting in the mid 1960s. Early examples include [[Robert Gunning (mathematician)|Robert Gunning]] and [[Hugo Rossi]]'s ''Analytic Functions of Several Complex Variables'' (1965){{r|gunning-rossi}}{{r|rudolph}} and [[Lynn Harold Loomis|Lynn Loomis]] and [[Shlomo Sternberg]]'s ''Advanced Calculus'' (1968).{{r|loomis-sternberg}} Initial adoption was sporadic, however, and most publishers continued using boldface. In 1979, [[Wiley (publisher)|Wiley]] recommended its authors avoid "double-backed shadow or outline letters, sometimes called blackboard bold", because they could not always be printed;{{r|wiley}} in 1982, Wiley refused to include blackboard bold characters in mathematical books because the type was difficult and expensive to obtain.{{r|krantz}}

[[Donald Knuth]] preferred boldface to blackboard bold and so did not include blackboard bold in the [[Computer Modern]] typeface that he created for the [[TeX]] mathematical typesetting system he first released in 1978.{{r|krantz}} When Knuth's 1984 ''[[The TeXbook]]'' needed an example of blackboard bold for the index, he produced <math>\mathrm{I\!R}</math> using the letters ''I'' and ''R'' with a negative space between;{{r|knuth}} in 1988 Robert Messer extended this to a full set of "poor man's blackboard bold" macros, overtyping each capital letter with carefully placed ''I'' characters or vertical lines.{{r|messer}}

Not all mathematical authors were satisfied with such workarounds. The [[American Mathematical Society]] created a simple chalk-style blackboard bold typeface in 1985 to go with the [[AMS-TeX]] package created by [[Michael Spivak]], accessed using the <code>\Bbb</code> command (for "blackboard bold"); in 1990, the AMS released an update with a new inline-style blackboard bold font intended to better match [[Times New Roman|Times]].{{r|amstex}} Since then, a variety of other blackboard bold typefaces have been created, some following the style of traditional inline typefaces and others closer in form to letters drawn with chalk.{{r|vieth}}

[[Unicode]] included the most common blackboard bold letters among the "[[Letterlike Symbols]]" in version 1.0 (1991), inherited from the [[Xerox Character Code Standard]]. Later versions of Unicode extended this set to all uppercase and lowercase [[Latin alphabet|Latin]] letters and a variety of other symbols, among the "[[Mathematical Alphanumeric Symbols]]".{{r|unicode}}

In professionally typeset books, publishers and authors have gradually adopted blackboard bold, and its use is now commonplace,{{r|krantz}} but some still use ordinary bold symbols. Some authors use blackboard bold letters on the blackboard or in manuscripts, but prefer an ordinary bold typeface in print; for example, [[Jean-Pierre Serre]] has used blackboard bold in lectures, but has consistently used ordinary bold for the same symbols in his published works.{{r|serre}} 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). The international standard [[ISO 80000-2]]:2019 lists {{math|'''R'''}} as the symbol for the real numbers but notes "the symbols {{math|1=<span style='letter-spacing: -.12em; padding: 0 .12em 0 0;'>IR</span>}} and <math>\R</math> are also used", and similarly for {{math|'''N'''}}, {{math|'''Z'''}}, {{math|'''Q'''}}, {{math|'''C'''}}, and {{math|'''P'''}} ([[prime numbers]]).{{r|iso}}