# counterexample

A *counterexample ^{}* is an example which is used to prove that a statement is false.

For instance, to disprove that the statement “For all $n$, ${2}^{{2}^{n}}+1$ is prime.”, one could exhibit $5$ as a counterexample; since ${2}^{{2}^{5}}+1=641\times 6700417$, the statement is false.

Title | counterexample |
---|---|

Canonical name | Counterexample |

Date of creation | 2013-03-22 14:43:00 |

Last modified on | 2013-03-22 14:43:00 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 5 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 00A20 |