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- Cantors_first_uncountability_proof abstract "Georg Cantor's first proof of uncountability demonstrates that the set of all real numbers is uncountably, rather than countably, infinite. This proof differs from the more familiar proof that uses his diagonal argument. Cantor's first uncountability proof was published in 1874, in an article that also contains a proof that the set of real algebraic numbers is countable, and a proof of the existence of transcendental numbers.Two points about which not all authors writing about Cantor's article have agreed are these: Is Cantor's proof of the existence of transcendental numbers constructive or non-constructive? Why did Cantor emphasize the countability of the real algebraic numbers rather than the uncountability of the real numbers?In 1891 Cantor published his diagonal argument, which produces an uncountability proof that is generally considered simpler and more elegant than his first proof. Both uncountability proofs contain ideas that can be used elsewhere. The diagonal argument is a general technique that is useful in mathematical logic and theoretical computer science, while Cantor's first uncountability proof can be generalized to any ordered set with the same order properties as the real numbers.".
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- Cantors_first_uncountability_proof wikiPageWikiLinkText "1874 uncountability proof".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "Cantor".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "Cantor's first uncountability proof".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "His proof".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "different method".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "earlier proved the uncountability of the reals by other methods".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "first proof".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "new method".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "original presentation".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "proved".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "proving".
- Cantors_first_uncountability_proof wikiPageWikiLinkText "showed".
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- Cantors_first_uncountability_proof subject Category:Georg_Cantor.
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