who is the mathematician who first use brackets to indicate grouping
Christopher Clavius
title: Bracket (mathematics) text: Bracket (mathematics) In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses ( ), square brackets [ ], braces { }, and angle brackets ⟨ ⟩. Generally such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take precedence over those surrounding it. Additionally, there are several uses and meanings for the various brackets. Historically, other notations, such as the vinculum, were similarly used for grouping; in present-day use, these notations all have specific meanings. The earliest use of brackets to indicate aggregation (i.e. title: Bracket (mathematics) text: 5(1 + 0) is 2 and 8 ÷ 4(2 + 0) is 1 and (2×3) + 4 is 10. This notation is extended to cover more general algebra involving variables: for example formula_2. Square brackets are also often used in place of a second set of parentheses when they are nested, to provide a visual distinction. Also in mathematical expressions in general, parentheses are used to indicate grouping (that is, which parts belong together) when necessary to avoid ambiguities, or for the sake of clarity. For example, in the formula (εη) = εη, used in the definition of composition of title: Bracket (mathematics) text: grouping) was suggested in 1608 by Christopher Clavius and in 1629 by Albert Girard. A variety of different symbols are used to represent angle brackets. In e-mail and other ASCII text it is common to use the less-than (codice_1) and greater-than (codice_2) signs to represent angle brackets, because ASCII does not include angle brackets. Unicode has three pairs of dedicated characters: In LaTeX the markup is codice_3 and codice_4: formula_1. In elementary algebra parentheses, ( ), are used to specify the order of operations. Terms inside the bracket are evaluated first; hence 2×(3 + 4) is 14 and 10 ÷ title: Bracket text: to refer to a specific type of bracket: in modern American usage, this is usually the square bracket and in modern British usage, this is usually the round bracket. Chevrons (⟨ ⟩) were the earliest type of bracket to appear in written English. Desiderius Erasmus coined the term "lunula" to refer to the rounded parentheses (), recalling the shape of the crescent moon. Some of the following names are regional or contextual. The characters ‹ › and « », known as or angular quote brackets, are actually quotation mark glyphs used in several European languages. Which one of each pair title: Bracket text: to indicate changes in indentation: Brackets are used in mathematics in a variety of notations, including standard notations for commutators, the floor function, the Lie bracket, equivalence classes, the Iverson bracket, and matrices. Square brackets may also represent closed intervals; formula_2 for example, represents the set of real numbers from 0 to 5 inclusive. Square brackets can also be used in chemistry to represent the concentration of a chemical substance in solution and to denote charge a Lewis structure of an ion (particularly distributed charge in a complex ion), repeating chemical units (particularly in polymers) and transition state structures, among