# Cantor normal form

###### Ordinal Normal Form (Cantor).

For ordinal numbers^{} $\alpha \mathrm{\ge}\mathrm{2}$ and $\gamma \mathrm{\ge}\mathrm{1}$ there is a unique $n$ such that there exist unique ${\beta}_{\mathrm{0}}\mathrm{>}\mathrm{\cdots}\mathrm{>}{\beta}_{n}$ and $$ such that $\gamma \mathrm{=}{\alpha}^{{\beta}_{\mathrm{0}}}\mathrm{\cdot}{\delta}_{\mathrm{0}}\mathrm{+}\mathrm{\cdots}\mathrm{+}{\alpha}^{{\beta}_{n}}\mathrm{\cdot}{\delta}_{n}$.

This theorem is often referred to as the *Cantor Normal Form of $\gamma $ in the base of $\alpha $*.

Title | Cantor normal form |
---|---|

Canonical name | CantorNormalForm |

Date of creation | 2013-03-22 15:33:01 |

Last modified on | 2013-03-22 15:33:01 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 9 |

Author | rspuzio (6075) |

Entry type | Theorem |

Classification | msc 03E10 |