It is demonstrated that quite unrestricted operation of conventional division by the real number zero can be implemented via multiplication by the – reciprocal to zero – ascending infinity in paired dual reciprocal spaces, provided that the “real” zero and the infinity are mutually reciprocal (i.e. multiplicatively inverse). Since the infinity is not an absolute concept independent of the particular circumstances in which it is being determined, the value of the setvalued infinity is not fixed but depends on an influence function that is usually applied for evaluation of integral kernels, the operations proposed here are always defined relative to a certain abstract influence function. The conceptual and operational validity of the proposed unrestricted division and multiplication by zero, is authenticated operationally by fairly simple example, using an evaluation of Frullani’s integral.
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