Operation (mathematics)

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In mathematicsan operation is a calculation from zero or more input values called operands to an output value. The number of operands is the arity of the operation.

An operation of arity zero, or 0-ary binare mathematische operationen is a constant. Generally, the arity is binare mathematische operationen to be finite, but infinitary operations are sometimes considered.

In this context, the usual operations, of finite arity are also called finitary operations. There are two common types of operations: Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include additionsubtractionmultiplicationdivisionand exponentiation. Operations can involve mathematical objects other than numbers. The logical values true binare mathematische operationen false can be combined using logic operationssuch as andor, and not.

Vectors can be added and subtracted. Rotations can be combined using the function composition operation, performing the first rotation and then the second. Operations on sets include the binary operations union and intersection and the unary binare mathematische operationen of complementation. Operations on functions include composition and convolution. Operations may not be defined for every possible value.

For example, binare mathematische operationen the real numbers one cannot divide by zero or take square roots of negative numbers. The values for which an operation is defined form a set called its domain. The set which contains the binare mathematische operationen produced is called the codomainbut the set of actual values attained by the operation is its range. For example, in the real numbers, the squaring operation only produces non-negative numbers; the codomain is the set of real numbers, but the range is the non-negative numbers.

Operations can involve dissimilar objects. A vector can be multiplied by a scalar binare mathematische operationen form another vector.

And the inner product operation on two vectors produces a scalar. An operation may or may not have certain properties, for example it may be associativecommutativeanticommutativeidempotentand so on.

The values combined are called operandsargumentsor inputsand the value produced is called the valueresultor output. Operations can have fewer or more than two inputs. Binare mathematische operationen operation is like an operatorbut the point of view is different. The sets X k binare mathematische operationen called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k the number of arguments is called the type or arity binare mathematische operationen the operation.

Thus a unary operation has arity one, and a binary operation has arity two. An operation of arity zero, called a nullary operation, is simply an element of the codomain Y.

An operation of arity k is called a k -ary operation. The above describes what is usually called a finitary operation, referring to the finite number of arguments the value k. There are obvious extensions where the arity is taken to be an infinite ordinal or cardinalor even an arbitrary set indexing the arguments.

Often, use of the term operation implies that the domain of the function is a power binare mathematische operationen the codomain i. From Wikipedia, the free encyclopedia. Not to be confused with Operator mathematics. This article needs additional citations for verification.

Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. January Learn how and when to remove this template message. A Course in Universal Algebra. Retrieved from " https: Elementary mathematics Algebra Arithmetic. Articles needing additional references from January All articles needing additional references.

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The word " bi nary" means composed of two pieces. A binary operation is simply a rule for combining two values to create a new value. The most widely known binary operations are those learned in elementary school: Let's take a look at some creative binary operations. It is possible to define "new" binary operations. Sometimes, a binary operation on a finite set a set with a limited number of elements is displayed in a table which shows how the operation is to be performed.

A binary operation on a set is a calculation involving two elements of the set to produce another element of the set. Not true for all real numbers. Not true for all reals. The table at the right shows the 16 possible answers using this operation. To read the table: The answer is the intersection point. What is 2 4? Unfortunately, you now need to check all of the other possibilities.

There is, however, a shorter way If the table is symmetric with respect to this line, the table is commutative. What is the identity element for the operation? Find the single element that will always return the original value. The identity element is 4. You will have found the identity element when all of the values in its row and its column are the same as the row and column headings.

Is associative for these values? Unfortunately, if you were asked the general question, "Is associative? Unlike the commutative property, there is NO shortcut for checking associativity when working with a table.

But remember, it only takes one arrangement which does not work to show that associativity fails. The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.

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