# example of bijection

It is known that the Cartesian product^{} of numerable sets are numerable, then the product^{} $\mathbb{N}\times \mathbb{N}$ is. Here we give an explicit mapping which does the task:

$$(n,m)\mapsto m+\frac{(n+m)(n+m+1)}{2}$$ |

It is almost easy to check bijectivity and curious how the elements of $\mathbb{N}\times \mathbb{N}$ are labeled.

Title | example of bijection |
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Canonical name | ExampleOfBijection |

Date of creation | 2013-03-22 16:30:18 |

Last modified on | 2013-03-22 16:30:18 |

Owner | juanman (12619) |

Last modified by | juanman (12619) |

Numerical id | 7 |

Author | juanman (12619) |

Entry type | Example |

Classification | msc 03-00 |

Related topic | ParingFunction |