[2] **viXra:1602.0198 [pdf]**
*submitted on 2016-02-16 21:38:55*

**Authors:** Florentin Smarandache

**Comments:** 107 Pages.

Welcome into my scientific lab!
My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific chats.
I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks.
In this book, one may find new and old questions and ideas, some of them already put at work, others dead or waiting, referring to various fields of research (e.g. from neutrosophic algebraic structures to Zhang's degree of intersection, or from Heisenberg uncertainty principle to neutrosophic statistics) – email messages to research colleagues, or replies, notes about authors, articles or books, so on.
Feel free to budge in the lab or use the scilogs as open source for your own ideas.

**Category:** Set Theory and Logic

[1] **viXra:1602.0006 [pdf]**
*replaced on 2016-08-29 12:45:44*

**Authors:** Andrew Banks

**Comments:** 20 Pages.

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.

**Category:** Set Theory and Logic