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

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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