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# 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 $\alpha$*.

Keywords:

ordinal, normal, Cantor, basis

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

03E10*no label found*

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