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For example, in the expression 3(x+y) the parentheses are symbols of grouping, but in the expression (3, 5) the parentheses may indicate an open interval. The most common symbols of grouping are the parentheses and the square brackets, and the latter are usually used to avoid too many repeated parentheses.
Symbols of grouping can be used to override the usual order of operations. [2] Grouped symbols can be treated as a single expression. [ 2 ] Symbols of grouping can be removed using the associative and distributive laws, also they can be removed if the expression inside the symbol of grouping is sufficiently simplified so no ambiguity results ...
In group theory and ring theory, square brackets are used to denote the commutator. In group theory, the commutator [g,h] is commonly defined as g −1 h −1 gh. In ring theory, the commutator [a,b] is defined as ab − ba. Furthermore, braces may be used to denote the anticommutator: {a,b} is defined as ab + ba.
The set is called the underlying set of the group, and the operation is called the group operation or the group law. A group and its underlying set are thus two different mathematical objects. To avoid cumbersome notation, it is common to abuse notation by using the same symbol to denote both. This reflects also an informal way of thinking ...
Various ways to cluster the number 8. The first or fifth mark in each group may be written at an angle to the others for easier distinction. In the fourth example, the fifth stroke "closes out" a group of five, forming a "herringbone". In the fifth row the fifth mark crosses diagonally, forming a "five-bar gate".
The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
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