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In mathematics and related subjects, understanding a mathematical expression depends on an understanding of symbols of grouping, such as parentheses (), square brackets [], and braces {} [1] (see note on terminology below). These same symbols are also used in ways where they are not symbols of grouping.
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 ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take ...
In mathematics this group is known as the dihedral group of order 8, and is either denoted Dih 4, D 4 or D 8, depending on the convention. This was an example of a non-abelian group: the operation ∘ here is not commutative , which can be seen from the table; the table is not symmetrical about the main diagonal.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra.
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
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.