## You are here

Homeiteration

## Primary tabs

# iteration

Let $f\colon X\to X$ be a function, $X$ being any set. The $n$-th iteration of a function is the function which is obtained if $f$ is applied $n$ times, and is denoted by $f^{n}$. More formally we define:

$f^{0}(x)=x$ |

and

$f^{{n+1}}(x)=f(f^{n}(x))$ |

for nonnegative integers $n$. If $f$ is invertible, then by going backwards we can define the iterate also for negative $n$.

Synonym:

iterate

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

26A18*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Info

## Corrections

Two things by digitalis ✓

comma by digitalis ✓

MSC by djao ✓

A few things. by Koro ✓

Typos and typesetting by bbukh ✓

comma by digitalis ✓

MSC by djao ✓

A few things. by Koro ✓

Typos and typesetting by bbukh ✓

## Versions

(v9) by mathwizard 2013-03-22