# iteration

Let $f:X\to X$ 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 $n$.

Title | iteration |
---|---|

Canonical name | Iteration |

Date of creation | 2013-03-22 12:43:40 |

Last modified on | 2013-03-22 12:43:40 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 9 |

Author | mathwizard (128) |

Entry type | Definition |

Classification | msc 26A18 |

Synonym | iterate |