Cantor’s Diagonal Proof

Marta Vlasáková



Cantor's diagonal proof is sig­nificant both because the central method of proof used in it has been subsequently applied in a number of other proofs, and because it is considered to confirm the existence of infinite sets whose size fun­ damentally and by an order of magnitude exceeds the size of the "classical" infinite set represented by all natural numbers, while their size can theoretically exceed every conceivable limit. Although Can­tor's proof is generally accepted by the scientific community, some experts are somewhat reserved about it. The aim of this paper is to present Cantor's proof in an accessible way, while pointing out its (hidden) assumptions and possible problematic points, and pointing out that some of its underlying assumptions are not indisputable mathematical truths, but rather postulated propositions that may or may not be accepted.


Cantor’s diagonal proof; ac­tual and potential infinity; real numbers; set cardinality; recursive function

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