THE CONTINUUM: A PROGRAM

(CONSTANT DIFFERENTIALS, STANDARD CALCULUS AND DIVISION BY ZERO)

Since Mathis’ constant differential calculus reveals that the standard analysis, whether infinitesimal or with limits, omits one or more physical dimensions from the description, such a calculus, by bringing back these missing dimensions, should be key to explaining the mysterious role of complex numbers in modern physics. The structure of correspondences between both forms of calculus, not less than their divergences, would help to understand complex analysis in the most general sense.

Just as after the triumph of the limit theory in calculus there was a comeback of infinitesimals, and not only in the non-standard version of Robinson’s calculus, but also in other alternative versions, advocators of division by zero and algebras with complete inverse function are now emerging. These algebras present new structures of interest for the treatment of rational numbers, which after all are the general domain of finite measurements and observable results in physics, and directly affect the integration of continuous and discrete computations.

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