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.

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Submission history

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

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