Operation (mathematics): Difference between revisions
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In mathematics, an Operator is usually defined as a [[Function (mathematics)|function]] which maps some finite [[Cartesian product]] of a set to itself. For instance, the [[real numbers]] form a set, and [[addition]] is a function mapping <math>\mathbb{R} \times \mathbb{R}</math> to <math>\mathbb{R}</math>. | In mathematics, an Operator is usually defined as a [[Function (mathematics)|function]] which maps some finite [[Cartesian product]] of a set to itself. For instance, the [[real numbers]] form a set, and [[addition]] is a function mapping <math>\mathbb{R} \times \mathbb{R}</math> to <math>\mathbb{R}</math>. | ||
In general, an operator + on a set A is a function of the form <math>+ : A^{k} \mapsto A</math>. We say that + is a k-ary operator, indicating the number of arguments it takes. In the case of real number addition, the operator is [[binary]] because it takes two arguments. | In general, an operator + on a set A is a function of the form <math>+ : A^{k} \mapsto A</math>. We say that + is a k-ary operator, indicating the number of arguments it takes. In the case of real number addition, the operator is [[binary]] because it takes two arguments. | ||
Revision as of 08:10, 12 November 2007
In mathematics, an Operator is usually defined as a function which maps some finite Cartesian product of a set to itself. For instance, the real numbers form a set, and addition is a function mapping to .
In general, an operator + on a set A is a function of the form . We say that + is a k-ary operator, indicating the number of arguments it takes. In the case of real number addition, the operator is binary because it takes two arguments.
