Discussion about Cantor’s first proof using the next-interval-function, potential and actual infinity. Cantor’s first proof of the uncountability of real numbers is the first rigorous demonstration of the notion of uncountability. Countable sets can be put into a list indexed with natural numbers. If a set cannot be listed, then, it has more members than the set of natural numbers and is uncountable. Cantor’s first proof is a proof by contradiction. First, he supposes that all real numbers are listed in any order by the list X=(x1, x2, x3 \u2026). Then, a real number out of this list is found by using a series of intervals, contradicting that X lists all real numbers.<\/p>\n
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PDF On Cantor’s first proof of uncountability Discussion about Cantor’s first proof using the next-interval-function, potential and actual infinity. Cantor’s first proof of the uncountability of real numbers is the first rigorous demonstration of the notion of uncountability. Countable sets can be put into a list indexed … Continue reading
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\nor Word https:\/\/www.academia.edu\/22104462\/On_Cantors_first_proof_of_uncountability<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"