- Operation theory
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In logic and mathematics, a finitary operation ω is a function of the form ω : X1 × … × Xk → Y. The sets Xj are the called the domains of the operation, the set Y is called the codomain of the operation, and the fixed non-negative integer k is called the arity of the operation. 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. Elements of the functional domains are called arguments. Elements of the codomain are called values.
An operation is often called an operator, though other users of the term may reserve it for more specialized uses. At any rate, the arguments are also called operands or inputs, and the values are also called results or outputs.
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