Set Theory and Logic


The Mythology of Infinity

Authors: Andrew Banks

Cantor’s infinity (CI) depends on the capability of completing an infinite collection of successive steps (ICSS). Otherwise, CI does not solve Zeno’s dichotomy paradox and all natural numbers cannot be upward constructed using the successor function. In spite of the fact that no one has ever scientifically witnessed an ICSS nor has anyone ever furnished a direct proof demonstrating its theoretical existence, the assumed capability of completing an ICSS rests at the foundations of theoretical mathematics. As such, this article will introduce a very general type of accelerated Turing machine that can execute instructions in any given time including zero seconds. This device will demonstrate that the assumption that an ICSS can be completed contradicts the assumption that the natural numbers are unbounded (NNU). Hence, CI is not consistent since it contains both. Furthermore, using this computing device and other machinery, it will be proven that space and time are only finitely divisible.

Comments: 20 Pages.

Download: PDF

Submission history

[v1] 2016-02-01 08:18:19
[v2] 2016-04-15 09:03:00
[v3] 2016-08-29 12:45:44

Unique-IP document downloads: 138 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