Often represents, in category theory, the interval category. In geometric algebra, represents the unit antiscalar, the identity element under the geometric antiproduct. Also used for the indicator function and the unit step function, and for the identity operator or identity matrix. Often represents, in set theory, the top element of a forcing poset, or occasionally the identity matrix in a matrix ring. (The Z is for Zahlen, German for "numbers", and zählen, German for "to count".) Occasionally used to denote an arbitrary metric space.
Represents a vector space or an affine variety generated by a set of polynomials. 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 for uppercase letters (e.g., R ), or the tropical semi-ring, or twistor space. In 2003, for the 15th edition, it stated that "open-faced (blackboard) symbols are reserved for familiar systems of numbers" (14.12). In 1993, for the 14th edition, it advised that "blackboard bold should be confined to the classroom" (13.14). The Chicago Manual of Style evolved over this issue. Serge Lang also used boldface instead of blackboard bold in his highly influential Algebra. ĭonald Knuth also preferred boldface to blackboard bold and so did not include blackboard bold in the Computer Modern fonts that he created for the TeX mathematical typesetting system. Jean-Pierre Serre used double-struck letters when he wrote bold on the blackboard, whereas his published works (like his well-known "Cohomologie galoisienne" ) have consistently used ordinary bold for the same symbols. Well-known books where the blackboard bold style is used include Lindsay Childs' A Concrete Introduction to Higher Algebra, which is widely used as a text for undergraduate courses in the US, John Stillwell's Elements of Number Theory, and Edward Barbeau's "University of Toronto Mathematics Competition (2001–2015)", which is often used to prepare for mathematics competitions. Many mathematicians adopted blackboard bold, but many others still prefer to use bold. In textbooks, however, the situation is not so clear cut. In the 1960s and 1970s, blackboard bold spread quickly in classrooms and is now widely used in the English- and French-speaking worlds. See Wikipedia's guide to writing better articles for further suggestions. Please improve the article by adding more descriptive text and removing less pertinent examples. This section may contain indiscriminate, excessive, or irrelevant examples.
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