https://DevOpsCloud.io -- Cloud Monk Losang Jinpa, Ph.D., MCSE/MCT, GitOps DevOps Engineer

In mathematics, an operation is a function that takes as input a fixed number of elements of a set and returns an element of the same set. For example, addition on real numbers is an operation that accepts two real numbers and returns a real number. In general, the input values may be called "operands" or "arguments". The number of operands is the arity of the operation. The arity is usually one of ${\displaystyle 0,1,2,\ldots }$.

The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity 0, or nullary operation, is a constant. The mixed product is an example of an operation of arity 3, also called ternary operation.

The four classical operations are addition, subtraction, multiplication, and division. These operations form the foundation of arithmetic and are essential for performing calculations and solving problems in various fields.

Generally, the arity is taken to be finite. However, infinitary operations are sometimes considered, in which case the "usual" operations of finite arity are called finitary operations.

A partial operation is defined similarly to an operation, but with a partial function in place of a function.