We prove that with the current axioms of commutative fields that are also complete metric spaces, there is an element ξ of these fields such that ξ∈{0} and ξ∉{0}. This implies that axioms defining such fields are not consistent and must be revisited. We achieve this result by proving the equivalence of two systems of differential equations. Picard-Lindelof theorem implies that one of the systems has a locally unique solution, and for the other, we prove that if a function x is a solution, so is the function x∘h if the function h satisfies certain minor conditions.

Some Differential Equations Lead to Inconsistencies in Mathematics (November 2016 version)

Some Differential Equations Lead to Inco[...]

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Some Differential Equations Lead to Inco[...]

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Some Differential Equations Lead to Inconsistencies in Mathematics (November 2013 version)

Some Differential Equations Lead to Inco[...]

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Some Differential Equations Lead to Inco[...]

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Main steps of the argument

Main steps of the argument-Jacques Bouhg[...]

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Main steps of the argument-Jacques Bouhg[...]

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