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Multiplicative inversions involving real zero and neverending ascending infinity in the multispatial framework of paired dual reciprocal spaces

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Inverses of complex numbers and of analytic functions are composites of mixed type for they are multiplicative inverses (i.e. reciprocals) of the modulus/magnitude combined with additive reverses of the argument/angle. Hence, the mixed inverses in the complex domain ℂ are not really reciprocals and therefore their lack of truly multiplicative reciprocity was a contributing reason that spurred the – unnecessary though still ongoing – prohibition of division by zero which is the natural reciprocal of the neverending ascending real infinity. Truly reciprocal algebraic operations are presented (via multiplicative algebraic inversions) by few examples within the new multispatial framework in terms of their abstract algebraic representations subscripted by the native algebraic bases of the mutually paired dual reciprocal (even though algebraic) spaces in which the inversive operations are performed.
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  • Science/Mathematics Education Department, Southern University and A&M College, Baton Rouge, LA 70813, USA
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