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

Authors: Arun Uday

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”.

Comments: 29 Pages.

Download: PDF

Submission history

[v1] 2018-07-24 22:55:24



Unique-IP document downloads: 301 times

Vixra.org 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. Vixra.org 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.

