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In mathematics, an operation is a function from a set to itself. For example, an operation on real numbers will take in real numbers and return a real number. An operation can take zero or more input values (also called "operands" or "arguments") to a well-defined output value.
A binary operation is a typical example of a bivariate function which assigns to each pair (,) the result . A multivariate function, multivariable function, or function of several variables is a function that depends on several arguments. Such functions are commonly encountered.
In mathematics, the composition operator takes two functions, and , and returns a new function ():= () = (()).Thus, the function g is applied after applying f to x.. Reverse composition, sometimes denoted , applies the operation in the opposite order, applying first and second.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The mathematical definition of an elementary function, or a function in elementary form, is considered in the context of differential algebra. A differential algebra is an algebra with the extra operation of derivation (algebraic version of differentiation).
An algebraic operation may also be defined more generally as a function from a Cartesian power of a given set to the same set. [4] The term algebraic operation may also be used for operations that may be defined by compounding basic algebraic operations, such as the dot product.
The hypergeometric function is an example of a four-argument function. The number of arguments that a function takes is called the arity of the function. A function that takes a single argument as input, such as f ( x ) = x 2 {\displaystyle f(x)=x^{2}} , is called a unary function .
The successor function is part of the formal language used to state the Peano axioms, which formalise the structure of the natural numbers.In this formalisation, the successor function is a primitive operation on the natural numbers, in terms of which the standard natural numbers and addition are defined. [1]