arXiv:0804.3199math.GM
Computable counter-examples to the Brouwer fixed-point theorem
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Abstract
This paper is an overview of results that show the Brouwer fixed-point theorem (BFPT) to be essentially non-constructive and non-computable. The main results, the counter-examples of Orevkov and Baigger, imply that there is no procedure for finding the fixed point in general by giving an example of a computable function which does not fix any computable point. Research in reverse mathematics has shown the BFPT to be equivalent to the weak König lemma in RCA$_0$ (the system of recursive comprehension) and this result is illustrated by relating the weak König lemma directly to the Baigger example.
> This is the standard nested interval proof It is not. I'll be honest: your one sentence response tells me you did not read the proof above in any detail. I chose Nelson's proof precisely because its construction is well-studied and well-understood. The same construction of a…
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