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Quote: the sequence of computable numbers is not computable because of the halting problem; get an infinite loop when processing its own description number

topics > all references > references t-z > QuoteRef: turiAM11_1936 , p. 246



Topic:
limitations of formalism
Topic:
Turing machine

Quotation Skeleton

It may be thought that arguments which prove … cannot be enumerable. It might, for instance, be … only true if the sequence of computable numbers … [Mentions that a diagonal argument proves that this is not possible, and then proves that one can not design a machine that determines whether or not the universal computing machine will halt on a particular input. Such a machine goes into an infinite loop when it tests its own description number.]   Google-1   Google-2

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Related Topics up

Topic: limitations of formalism (92 items)
Topic: Turing machine (30 items)

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