# partial function

A function $f:A\to B$ is sometimes called a *total function ^{}*, to signify that $f(a)$ is defined for every $a\in A$. If $C$ is any set such that $C\supseteq A$ then $f$ is also a

*partial function*from $C$ to $B$.

Clearly if $f$ is a function from $A$ to $B$ then it is a partial function from $A$ to $B$, but a partial function need not be defined for every element of its domain. The set of elements of $A$ for which $f$ is defined is sometimes called the *domain of definition*.

Title | partial function |
---|---|

Canonical name | PartialFunction |

Date of creation | 2013-03-22 12:58:15 |

Last modified on | 2013-03-22 12:58:15 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 11 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03E20 |

Defines | total function |

Defines | domain of definition |