Functions and Analysis


Real Numbers in the Neighborhood of Infinity

Authors: Jonathan W. Tooker

We demonstrate the existence of a broad class of real numbers which are not elements of any number field: those in the neighborhood of infinity. After considering the reals and the affinely extended reals, we prove that numbers in the neighborhood of infinity are ordinary real numbers of the type detailed in Euclid's Elements. We show that real numbers in the neighborhood of infinity obey the Archimedes property of real numbers. The main result is an application in complex analysis. We show that the Riemann zeta function has infinitely many non-trivial zeros off the critical line in the neighborhood of infinity.

Comments: 32 Pages.

Download: PDF

Submission history

[v1] 2018-11-14 17:09:09
[v2] 2018-11-16 21:03:52
[v3] 2018-11-18 01:28:07
[v4] 2018-11-23 21:14:57
[v5] 2018-12-10 09:38:19
[v6] 2019-06-27 21:04:14
[v7] 2019-08-17 15:44:20
[v8] 2019-10-27 16:08:48

Unique-IP document downloads: 1362 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus