A definable number which cannot be approximated algorithmically

Nicolas Brener

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arXiv · 1003.0480

A definable number which cannot be approximated algorithmically

Nicolas Brener

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Abstract

The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all) known non-computable numbers are approachable by TMs. Then an example of a number not approachable by a TM is given.

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Nicolas Brener. 2010-03-01. A definable number which cannot be approximated algorithmically. https://arxiv.org/abs/1003.0480

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