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Braces { } are used to identify the elements of a set. For example, {a,b,c} denotes a set of three elements a, b and c. Angle brackets are used in group theory and commutative algebra to specify group presentations, and to denote the subgroup or ideal generated by a collection of elements.
Set-builder notation: denotes the set whose elements are listed between the braces, separated by commas. Set-builder notation : if P ( x ) {\displaystyle P(x)} is a predicate depending on a variable x , then both { x : P ( x ) } {\displaystyle \{x:P(x)\}} and { x ∣ P ( x ) } {\displaystyle \{x\mid P(x)\}} denote the set formed by the values ...
braces, a.k.a. curly brackets (for set notation) 1895 ... arrow (for function notation) 1936 (to denote images of specific elements) Øystein Ore:
Braces (curly brackets) first became part of a character set with the 8-bit code of the IBM 7030 Stretch. [7] In 1961, ASCII contained parentheses, square, and curly brackets, and also less-than and greater-than signs that could be used as angle brackets.
The simplest way to describe a set is to list its elements between curly braces (known as defining a set extensionally). Thus {1, 2} denotes the set whose only elements are 1 and 2. (See axiom of pairing.) Note the following points: The order of elements is immaterial; for example, {1, 2} = {2, 1}.
The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page.
A set of coordinates in a coordinate system; Tuple, a sequence of elements; The greatest common divisor of two numbers; Equivalence class congruence, especially for modular arithmetic or modulo an ideal; A higher order derivative in Lagrange's notation; Binomial or multinomial coefficient
Deutsch: Dieses Dokument listet 20323 Symbole und die dazugehörigen LaTeX-Befehle auf. Manche Symbole sind in jedem LaTeX-2ε-System verfügbar; andere benötigen zusätzliche Schriftarten oder Pakete, die nicht notwendig in jeder Distribution mitgeliefert werden und daher selbst installiert werden müssen.