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Cantor's diagonal argument

Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers. Such sets are now called uncountable sets…

Uncountable set, Consequences & Overview

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Uncountable set

Consequences

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Cantor's diagonal argument

Nodes73
Edges72
Triples4
Avg. degree1.97
Density0.027397
Components1

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set displaystyle also sets uncountable numbers bijection proof diagonal mathbb cantor function cantor's argument theory injection constructive existence mathcal infinite

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SubjectPredicateObjectConfidenceSrc
the negation of Cantor's preorderinstance ofas opposed to alternatives0.80text
or a definition in terms of assigned ordinalsinstance ofas opposed to alternatives0.80text
2 Ninstance ofUncountable sets0.80text
the non-existence of a set of all sets may or may not remain valid.Analogues of the diagonal argument are widely used in mathematics to prove the existence or nonexistence of certain objectsinstance ofarguments0.80text

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