Questions about Cantor's first uncountability proof and the definition of R

Asked May 15 '24 at 13:14

Active May 15 '24 at 13:14

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I have a question about Cantor's first uncountability proof.

What definition of $\mathbb{R}$ did Cantor use in his proof? Is that, for example, build on the axiom about bounded sets or build on the axiom formulated using interval nests?

I tried to find it in the original proof, but I can't find it. Who can help me with a good source?

Maybe anyone can help me, thanks in advance!

asked May 15 '24 at 13:14

Marco

See Bibliography: Cantor (1874) – Mauro ALLEGRANZA May 15 '24 at 13:23
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Cantor's def of reals (1872) – Mauro ALLEGRANZA May 15 '24 at 13:24
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Google phrase search for the title of Cantor's first (1874) paper: Ueber eine eigenschaft des inbegriffes aller reellen algebraischen zahlen. For various published translations of Cantor's papers, see the answers to Does There Exist a LaTeX/Word Rewrite of Georg Cantor's Works?. – Dave L. Renfro May 15 '24 at 13:28

Questions about Cantor's first uncountability proof and the definition of R

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