Functions and Analysis


Non-Trivial Extension of Real Numbers

Authors: Ilya Chernykh

We propose an extension of real numbers which reveals a surprising algebraic role of Bernoulli numbers, Hurwitz Zeta function, Euler-Mascheroni constant as well as generalized summations of divergent series and integrals. We extend elementary functions to the proposed numerical system and analyze some symmetries of the special elements. This reveals intriguing closed-form relations between trigonometric and inverse trigonometric functions. Besides this we show that the proposed system can be naturally used as a cardinality measure for fine comparison between infinite countable sets in metric space which respects the intuitive notion of the set's size.

Comments: 11 Pages.

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Submission history

[v1] 2017-01-26 01:27:43
[v2] 2017-02-01 10:10:22
[v3] 2017-04-27 23:34:08
[v4] 2017-05-12 07:46:53
[v5] 2017-05-18 05:57:40
[v6] 2018-11-10 13:58:15

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