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In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable. The concept of function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

### Definition

### Notation

### Other terms

### Specifying a function

### Representing a function

### General properties

### Multivariate function

### In calculus

### Function space

### Multi-valued functions

### In the foundations of mathematics and set theory

### In computer science