Operation ( mathematics ) - wikipedia Operation ( mathematics ) 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 2016 ) Elementary arithmetic operations : +, plus ( addition ) −, minus ( subtraction ) ÷, obelus ( division ) ×, times ( multiplication ) In mathematics, an 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. The most commonly studied operations are binary operations of arity 2, such as addition and multiplication, and unary operations of arity 1, such as additive inverse and multiplicative inverse. An operation of arity zero, or 0 - ary operation is a constant. The mixed product is an example of an operation of arity 3, or ternary operation. Generally, the arity is supposed to be finite, but infinitary operations are sometimes considered. In this context, the usual operations, of finite arity are also called finitary operations. Contents 1 Types of operation 2 General description 3 See also 4 Notes Types of operation A binary operation takes two arguments x ( displaystyle x ) and y ( displaystyle y ) and returns the result x ∘ y ( displaystyle x circ y ) There are two common types of operations : unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation. Operations can involve mathematical objects other than numbers. The logical values true and false can be combined using logic operations, such as and, or, 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 operation of complementation. Operations on functions include composition and convolution. Operations may not be defined for every possible value. For example, in the real numbers one can not 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 values produced is called the codomain, but 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 to 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 associative, commutative, anticommutative, idempotent, and so on. The values combined are called operands, arguments, or inputs, and the value produced is called the value, result, or output. Operations can have fewer or more than two inputs. An operation is like an operator, but the point of view is different. For instance, one often speaks of `` the operation of addition '' or `` addition operation '' when focusing on the operands and result, but one says `` addition operator '' ( rarely `` operator of addition '' ) when focusing on the process, or from the more abstract viewpoint, the function + : S × S → S. General description An operation ω is a function of the form ω : V → Y, where V ⊂ X ×... × X. The sets X are 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 of 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. Thus a k - ary operation is a ( k + 1 ) - ary relation that is functional on its first k domains. 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 cardinal, or even an arbitrary set indexing the arguments. Often, use of the term operation implies that the domain of the function is a power of the codomain ( i.e. the Cartesian product of one or more copies of the codomain ), although this is by no means universal, as in the example of multiplying a vector by a scalar. See also Hyperoperation Order of operations Notes Jump up ^ Burris, S.N. ; Sankappanavar, H.P. ( 1981 ). `` Chapter II, Definition 1.1 ''. A Course in Universal Algebra. Springer. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Operation_(mathematics)&oldid=809729773 '' Categories : Elementary mathematics Algebra Arithmetic Hidden categories : Articles needing additional references from January 2016 All articles needing additional references Talk Contents About Wikipedia Català Čeština Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français Galego 한국어 Հայերեն Italiano Македонски Nederlands 日本 語 Norsk Norsk nynorsk Português Русский Sicilianu Simple English Slovenčina Slovenščina Српски / srpski Srpskohrvatski / српскохрватски Svenska தமிழ் ไทย Türkçe Українська Tiếng Việt ייִדיש 中文 Edit links This page was last edited on 11 November 2017, at 00 : 56. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia ® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. About Wikipedia

Question: a calculation from input values such as add subtract multiply and divide
Answer: operation