# ordered pair

For any sets $a$ and $b$, the ordered pair $(a,b)$ is the set $\{\{a\},\{a,b\}\}$.

The characterizing property of an ordered pair is:

$$(a,b)=(c,d)\iff a=b\text{and}c=d,$$ |

and the above construction of ordered pair, as weird as it seems, is actually the simplest possible formulation which achieves this property.

Title | ordered pair |
---|---|

Canonical name | OrderedPair |

Date of creation | 2013-03-22 11:48:53 |

Last modified on | 2013-03-22 11:48:53 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 9 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 03-00 |

Classification | msc 70A05 |

Classification | msc 70G99 |