Remarks about Cantor's Theorem

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Conference Proceeding

Streaming Media

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In 1890, Cantor produced his famed theorem about the infinity of infinite cardinalities with the declared intention to give a new, very abstract proof of his other theorem of 1874 about the two distinct cardinalities of the set of natural numbers and of the set of real numbers. And certainly one proof is strikingly different from the other. The earlier result was just a technical lemma to obtain a result about transcendental numbers – a renowned theorem in the mathematical circles, though rarely associated with Cantor.

We present the two proofs in contemporary mathematical language, and show how Cantor's second approach applies directly to several other paradoxical situations.


This presentation was part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics in spring 2024.