Set Theory and Logic


Refutation of Constructive Brouwer Fixed Point Theorem © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III

We construct the Brouwer fixed point theorem (BFPT) as implications of four variables as the antecedent. Because the consequent is composed of disjunctions of ordered pairs, the totality of ordered combinations requires that the argument connective is equivalence. The result is not tautologous and refutes BFPT using a constructive proof. (If the consequent is taken as a multiplicity of ordered combinations, the equivalence connective and the implication connective share the same table result which deviates further from tautology.) We conclude that BFPT is mislabeled as a theorem, as non constructively based on set theory, and correctly named as the Brouwer fixed point conjecture (BFPC).

Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-servcies dot com

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[v1] 2018-06-09 22:49:48

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