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2020 | 144 | 56-69
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Pairing of infinitesimal descending complex singularity with infinitely ascending, real domain singularity

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EN
Pairing of infinitesimal descending singularity of the 2D domain of complex numbers with an infinitely ascending singularity deployed in the 1D domain of real numbers, where the real singularity can be equated operationally with never-ending, whether countable or not, infinity, requires the employment of a pair of mutually dual reciprocal spaces in order for each of the spaces of the twin quasigeometric structure to be truly operational. Creation of twin quasigeometric structures comprising paired dual reciprocal spaces that are really operational and truly invertible, is the necessary condition for making the notion of operationally sound infinity viable. Although acceptance of the multispatial reality paradigm seems optional, it is shown that even performing legitimate scalar differentiation (in accordance with product differentiation rule) can yield either incomplete or incorrect evaluations of compounded scalar functions. This curious fact implies inevitable need for awareness of conceptual superiority of the multispatial reality paradigm over the former, unspoken and thus unchallenged in the past, single-space reality paradigm, in order to prevent even inadvertent creation of formwise illegitimate, or just somewhat incomplete, pseudodifferentials, which can be obtained even with the use of quite legitimate operational rules of scalar differential calculus.
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144
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56-69
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  • Science/Mathematics Education Department, Southern University and A&M College, Baton Rouge, LA 70813, USA
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article
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bwmeta1.element.psjd-16bb09fe-b24e-495e-9cce-3f78f92b9410
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