Binary operation/Computing operation/Introduction/Section

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We consider the mathematical operations addition and multiplication, within the real numbers, as mappings

so we assign to each pair

the real number (and respectively). Such a mapping is called an operation.

An operation (or binary operation) on a set is a mapping

The domain of an operation is thus the product set of with itself, and the range is also . Addition, multiplication and subtraction (on , on , or on ) are operations. On and , the division is not an operation, since it is not defined in case the second component equals . However, the division is an operation on .