# Cantor normal form

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

For ordinal numbers $\alpha\geq 2$ and $\gamma\geq 1$ there is a unique $n$ such that there exist unique $\beta_{0}>\cdots>\beta_{n}$ and $0<\delta_{0}<\alpha,\ldots,0<\delta_{n}<\alpha$ such that $\gamma=\alpha^{\beta_{0}}\cdot\delta_{0}+\cdots+\alpha^{\beta_{n}}\cdot\delta_% {n}$.

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

Title Cantor normal form CantorNormalForm 2013-03-22 15:33:01 2013-03-22 15:33:01 rspuzio (6075) rspuzio (6075) 9 rspuzio (6075) Theorem msc 03E10