# fix

In mathematical statements, mathematical objects such as points and numbers are described as being *fixed*. A possible meaning for this usage is that the mathematical object in question is not allowed to vary throughout the statement or proof (or, in some cases, a portion thereof). Although a fixed object typically does not vary, it is almost always arbitrary. This may seem paradoxical, but it is quite logical: An object is chosen arbitrarily, then it is never allowed to vary. See the entry betweenness in rays for an example of this usage.

The usage of the *fix* and *fixed* may also that a mapping sends the mathematical object to itself. These two usages are technically not the same. The former usage (described in the previous paragraph) states a property of the mathematical object in question and is always either part of an implication^{} (as in “If $x\in \mathbb{R}$ is fixed, then…”) or a command made by the author to the reader (as in “Let $x\in \mathbb{R}$ be fixed.” and “Fix $x\in \mathbb{R}$.”). The latter usage (described in this paragraph) states a property of a mapping and may or may not be part of a conditional^{} statement or a command. The word “fixes” *always* refers to this usage (as in “Note that $f$ fixes $x$.”). See the entry fix (transformation actions) (http://planetmath.org/Fixed) for a further explanation of the latter usage.

Title | fix |
---|---|

Canonical name | Fix |

Date of creation | 2013-03-22 16:11:19 |

Last modified on | 2013-03-22 16:11:19 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 6 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 03-00 |

Classification | msc 03F07 |

Synonym | fixed |

Related topic | Fixed |