## Abstract

Informally, a function *f* is described by a formula or a rule which, for a given input (usually a real number *x*), determines uniquely an output (again typically a real number *y*). The input is supposed to be an element of a set *A* called the domain of the function, and the output belongs to a set *B* called the codomain. When this happens we write *y* = *f* (*x*) and *f*: *A* → *B.* Examples of functions of this sort with *A* = *B* = ℝ (the set of all real numbers) are given for instance by (i) *y* = *f*(*x*) = *x*^{2} + 1, (ii) *y* = *g*(*x*) = 1 if *x* ≥ 0, = 0 if *x* < 0, (iii) *y* = *h*(*x*) = the smallest prime number ≥ *x.* Many more examples will be given in the first section of this chapter.

## Keywords

Unit Circle Rational Number Monotone Function Infinite Limit Staircase Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag London 2004