Functions and Analysis

    

Complete Integers: Extending Integers to Allow Real Powers Have Discontinuities in Zero

Authors: Davide Peressoni

We will define a superset of integers (the complete integers), which contains the dual of integers along parity (e.g. the odd zero, the even one, ...). Then we will see how they form a ring and how they can be used as exponents for real numbers powers, in order to write functions which have a discontinuity in zero (the function itself or one of its derivates), as for example |x| and sgn(x).

Comments: 8 Pages.

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Submission history

[v1] 2023-12-31 20:26:57

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