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After serious thinking WM wrote :You are misinformed. 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:On 25.02.2025 11:50, FromTheRafters wrote:He didn't,joes presented the following explanation :>>WDYM "further"? Induction goes up to infinity.>
With von Neumann's construction of ordinals it can be extended to transfinite ordinal numbers. Zermelo's construction cannot be extended this way.
How could Cantor use transfinite induction then?
he merely showed that a countable list could not contain every real number.He showed a lot more.
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