Re: The set of necessary FISONs

On 26.02.2025 15:42, FromTheRafters wrote:

WM pretended :

 Consider Cantor's first application of transfinite induction in order to determine the power function in the second number class [G. Cantor: "Beiträge zur Begründung der transfiniten Mengenlehre 2", Math. Annalen 49 (1897) § 18. Cantor, p. 336ff]. In English:
https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf, p. 52.
>

he merely showed that a countable list could not contain every real number.

>
He showed a lot more.

 https://mathresearch.utsa.edu/wiki/index.php?title=Natural_Numbers:Postulates#Zermelo_ordinals
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Each natural number is then equal to the set containing just the natural number preceding it. This is the definition of Zermelo ordinals. Unlike von Neumann's construction, the Zermelo ordinals do not account for infinite ordinals.

Wrong. Zermelo began to work on the problems of set theory under Hilbert's influence and in 1902 published his first work concerning the addition of transfinite cardinals. His ω is the first transfinite ordinal.

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Finite "Mathematical Induction" but not infinite "Transfinite Induction" so Cantor likely used von Neumann's construction.

Nonsense.
Regards, WM