# example of infinite hyperreal number

The hyperreal number ${\{n\}}_{n\in \mathbb{N}}\in {}^{*}\mathbb{R}$ is (or ).

Proof : Let $\mathcal{F}$ be the nonprincipal ultrafilter^{} in the entry (http://planetmath.org/Hyperreal).

Given any positive $a\in \mathbb{R}$ we have that $\{n\in \mathbb{N}:n\le a\}$ is finite, so $$ and therefore $$.

Thus ${\{n\}}_{n\in \mathbb{N}}$ is infinite^{}.$\mathrm{\square}$

Title | example of infinite hyperreal number |
---|---|

Canonical name | ExampleOfInfiniteHyperrealNumber |

Date of creation | 2013-03-22 17:25:59 |

Last modified on | 2013-03-22 17:25:59 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 5 |

Author | asteroid (17536) |

Entry type | Example |

Classification | msc 26E35 |