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2020 | 149 | 23-35
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Quaternionic operational infinity

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By analogy to the complex analytic representation of infinity that I have already proposed in my prior paper, it is demonstrated here by examples that a hypercomplex representation of infinity can also be conjectured and formulated in a formwise similar way. Unlike the two-dimensional (2D) complex infinity, which holds in 2D spaces equipped with an orthogonal homogeneous algebraic basis, the 4D quaternionic infinity requires an algebraic or quasigeometric basis that would be either heterogenous if established within a single space or, if it would be established upon a quasigeometric multispatial structure then at least two homogeneous bases are needed for the latter structure. In the latter case orthogonality and isometry are preserved. The multispatiality not only conforms to the experimentally confirmed reality of the quantum Cheshire Cat whose grin was located in a separate beam path from the beam path of the cat but also implies the feasibility of prospective mathematical reformulation of the basically complex (and thus essentially 2D) quantum mechanics in terms of certain hypercomplex 4D quasispatial structures under auspices of the multispatial reality paradigm.
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  • Science/Mathematics Education Department, Southern University and A&M College, Baton Rouge, LA 70813, USA
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