# structure of finite hyperreal numbers

Theorem - Every (or ) hyperreal number $x\in {}^{*}\mathbb{R}$ admits a unique of the form

$$x=a+\u03f5$$ |

where $a\in \mathbb{R}$ and $\u03f5$ is infinitesimal^{}.

Remark : This theorem just says that every finite hyperreal number has a real part^{} and an infinitesimal part (just like real and imaginary parts in complex numbers^{}).

Title | structure of finite hyperreal numbers |
---|---|

Canonical name | StructureOfFiniteHyperrealNumbers |

Date of creation | 2013-03-22 17:26:02 |

Last modified on | 2013-03-22 17:26:02 |

Owner | asteroid (17536) |

Last modified by | asteroid (17536) |

Numerical id | 4 |

Author | asteroid (17536) |

Entry type | Theorem |

Classification | msc 26E35 |