# Burali-Forti paradox

The *Burali-Forti* paradox^{} demonstrates that the class of all ordinals^{} is not a set. If there were a set of all ordinals, $Ord$, then it would follow that $Ord$ was itself an ordinal, and therefore that $Ord\in Ord$. if sets in general are allowed to contain themselves, ordinals cannot since they are defined so that $\in $ is well founded over them.

This paradox is similar to both Russell’s paradox and Cantor’s paradox, although it predates both. All of these paradoxes prove that a certain object is “too large” to be a set.

Title | Burali-Forti paradox^{} |
---|---|

Canonical name | BuraliFortiParadox |

Date of creation | 2013-03-22 13:04:28 |

Last modified on | 2013-03-22 13:04:28 |

Owner | Henry (455) |

Last modified by | Henry (455) |

Numerical id | 8 |

Author | Henry (455) |

Entry type | Definition |

Classification | msc 03-00 |