# empty set

An empty set^{} is a set $\mathrm{\varnothing}$ that contains no elements. The Zermelo-Fraenkel Axioms^{} of set theory^{} imply that there exists an empty set. One constructs an empty set by starting with any set $X$ and then applying the axiom of separation to form the empty set $\mathrm{\varnothing}:=\{x\in X\mid x\ne x\}$.

An empty set is a subset of every other set, and any two empty sets are equal. Alternative notations^{} for the empty set include $\{\}$ and $\mathrm{\varnothing}$.

Title | empty set |
---|---|

Canonical name | EmptySet |

Date of creation | 2013-03-22 11:49:55 |

Last modified on | 2013-03-22 11:49:55 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 8 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 03-00 |

Classification | msc 65H05 |

Classification | msc 65H10 |

Synonym | null set |