# Cantor’s theorem

Let $X$ be any set and $\mathcal{P}(X)$ its power set^{}. Then there is no bijection between $X$ and $\mathcal{P}(X)$. Moreover, the cardinality of $\mathcal{P}(X)$ is strictly greater than that of $X$; that is, $$.

Title | Cantor’s theorem |
---|---|

Canonical name | CantorsTheorem |

Date of creation | 2013-03-22 12:44:50 |

Last modified on | 2013-03-22 12:44:50 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 8 |

Author | Wkbj79 (1863) |

Entry type | Theorem |

Classification | msc 03E17 |

Classification | msc 03E10 |

Related topic | CantorsDiagonalArgument |

Related topic | KonigsTheorem |