Cantor normal form theorem: Difference between revisions

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#REDIRECT [[Ordinal arithmetic#Cantor normal form]]

The '''Cantor normal form theorem''' is a theorem about [[ordinal arithmetic]] proven by [[Georg Cantor]] in 1897. It states that for every ordinal <math>\alpha>0</math>, there exist unique ordinals <math>\alpha_0,\alpha_1,\ldots,\alpha_n</math> for some <math>n\in\mathbb N</math>, such that <math>\alpha_0\ge\alpha_1\ge\ldots\alpha_n</math> and <math>\omega^{\alpha_0}+\omega^{\alpha_1}+\cdots+\omega^{\alpha_n}=\alpha</math>.<ref>M. Rathjen, [The Art of Ordinal Analysis https://www1.maths.leeds.ac.uk/~rathjen/ICMend.pdf] (p.4).</ref>

==References==