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A function is a mathematical concept that assigns to each element of a set exactly one element of another set. Learn the history, definition, types, properties, and examples of functions in mathematics.
A functional is a certain type of function that maps a space of functions into the field of real or complex numbers. Learn about different types of functionals, such as linear, non-linear, local, and global, and their applications in calculus, physics, and computer science.
A function, procedure, method, or routine (also known as a subprogram) is a callable unit of software logic that can be invoked multiple times. Learn about the history, terminology, and implementation of subprograms in different programming languages and environments.
Learn the definition, examples and properties of the graph of a function, which is the set of ordered pairs of its domain and codomain. See how to plot functions of one or two variables on a Cartesian plane or space.
Learn how the mathematical concept of a function evolved from the 17th to the 19th century, from analytic expressions to single-valued mappings. Explore the contributions of mathematicians such as Leibniz, Euler, Fourier and Cauchy to the development of the function theory.
Learn about the different properties and classifications of functions in mathematics, such as injective, surjective, bijective, continuous, differentiable, analytic, etc. See examples, definitions and references for each type of function.
Colloquially, the "function" is also called ambiguous at point (although there is per definitionem never an "ambiguous function"), and the original "definition" is pointless. Despite these subtle logical problems, it is quite common to use the term definition (without apostrophes) for "definitions" of this kind, for three reasons:
An elementary function is a function of a single variable that can be built from polynomial, rational, trigonometric, hyperbolic, and exponential functions and their inverses. Learn the definition, examples, closure properties, and differential algebra of elementary functions.