Set Theory and Logic

1807 Submissions

[2] viXra:1807.0418 [pdf] replaced on 2018-09-24 22:11:51

Visualizing the Escape Paths of Quaternion Fractals

Authors: Shawn Halayka
Comments: 8 Pages.

The escape paths of the points in some quaternion fractal sets are visualized.
Category: Set Theory and Logic

[1] viXra:1807.0417 [pdf] submitted on 2018-07-24 22:55:24

A Dual Identity Based Symbolic Understanding of the Gödel’s Incompleteness Theorems, P-NP Problem, Zeno’s Paradox and Continuum Hypothesis

Authors: Arun Uday
Comments: 29 Pages.

A semantic analysis of formal systems is undertaken, wherein the duality of their symbolic definition based on the “State of Doing” and “State of Being” is brought out. We demonstrate that when these states are defined in a way that opposes each other, it leads to contradictions. This results in the incompleteness of formal systems as captured in the Gödel’s theorems. We then proceed to resolve the P-NP problem, which we show to be a manifestation of Gödel’s theorem itself. We then discuss the Zeno’s paradox and relate it to the same aforementioned duality, but as pertaining to discrete and continuous spaces. We prove an important theorem regarding representations of irrational numbers in continuous space. We extend the result to touch upon the Continuum Hypothesis and present a new symbolic conceptualization of space, which can address both discrete and continuous requirements. We term this new mathematical framework as “hybrid space”.
Category: Set Theory and Logic