Functions and Analysis


Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis

Authors: Jonathan W. Tooker

Recent analysis has uncovered a broad swath of previously unconsidered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of this paper include (1) to prove that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. The methods used in this analysis include nothing other than basic arithmetic, a little trigonometry, and Euclidean geometry. In addition to the zeros used to disprove the Riemann hypothesis in earlier work, here we present yet more zeros which independently constitute the negation of the Riemann hypothesis.

Comments: 66 Pages. This paper is undergoing some syntactical changes/improvements. The paper is fine as is, but there are some issues which are currently being improved. In the meantime, readers are directed to the finalized verisons of viXra:1811.0222 and viXra:1809.0234

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Submission history

[v1] 2019-06-13 14:10:23

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