Numbers Defined by Turing Machines
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We consider three types of Turing machines defining functions on infinite words and investigate some characteristic properties of these types of Turing machine mappings. Using the interpretation of infinite words as the expansions of numbers we obtain three classes of real respectively complex numbers. We prove that the three classes of complex numbers form algebraically closed subfields of the field of complex numbers.
KeywordsRecursive Relation Turing Machine Recursive Function Real Polynomial Input Tape
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