What is a function?

In mathematics and computer science, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example of this is the function that relates each real number x to its square x^2. The output of a function can depend not only on the input but also on the function’s definition.

The concept of a function is fundamental in mathematics and is used in nearly every branch of modern science and engineering. It serves as a building block for mathematical analysis, which is the study of change and motion. In programming, a function is also referred to as a subroutine, procedure, or method, depending on the programming language. It is a sequence of program instructions that performs a specific task, packaged as a unit. This unit can be used in programs wherever that particular task should be performed.

Functions are defined by their name, parameters (if any), the type of value they return (if they return a value), and their body, which is a block of code that defines what the function does. Functions provide modularity and reusability in programming, allowing for more manageable code and helping to reduce redundancy.

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