# upper bound

Let $S$ be a set with a partial ordering $\le $, and let $T$ be a subset of $S$.
An upper bound^{} for $T$ is an element $z\in S$ such that $x\le z$ for all $x\in T$. We say that $T$ is bounded from above if there exists an upper bound for $T$.

Lower bound, and *bounded from below* are defined in a similar manner.

Title | upper bound |

Canonical name | UpperBound |

Date of creation | 2013-03-22 11:52:15 |

Last modified on | 2013-03-22 11:52:15 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 9 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 06A06 |

Classification | msc 11A07 |

Defines | bound |

Defines | lower bound |

Defines | bounded |

Defines | bounded from above |

Defines | bounded from below |