PlanetMath: Cantor normal form

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Cantor normal form

(Theorem)

Ordinal Normal Form 1 (Cantor) For ordinal numbers $\alpha\geq 2$ and $\gamma\geq 1$ there is a unique 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 $\alpha$ .

"Cantor normal form" is owned by rspuzio. [ full author list (2) | owner history (1) ]

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Keywords:

ordinal, normal, Cantor, basis

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Cross-references: base, ordinal numbers, normal form
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This is version 6 of Cantor normal form, born on 2005-10-27, modified 2006-10-19.
Object id is 7448, canonical name is CantorNormalForm.
Accessed 1452 times total.

Classification:

AMS MSC:

03E10 (Mathematical logic and foundations :: Set theory :: Ordinal and cardinal numbers)

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