Set Theory and Logic

Time & Relativity in Mathematics

Authors: Pankaj Mani
Comments: 24 Pages.

In this paper, we try to revisit some of the most fundamental issues lying at the foundation of mathematics in space-time relativistic perspective ,rather than conventional absolute space. We are adding a new dimension "Time" to the mathematics and review it in Space-Time relativistic framework to resolve the major foundational issues and making it in line with physical world realities. We shall look at the famous Cantor’s Diagonalization approach in to show the Countability of Real Numbers and explain Infiniteness in that perspective. We shall also look to resolve the famous paradoxes e.g. Richard, Russell,Liar, Skolem. We shall also look at the foundation of Set theory historically in Space-time to restore the issues that had led to ZFC by elimination and restrictions. As a consequence, we shall also revisit Godel Incompleteness theorems for Real Numbers and also otherwise explain the "inconsistency" in the new relativistic framework where they might be extended to all relativistically. This could possibly lead to entirely new way of looking at conventional mathematics in broad sense where reference frame plays key role in mathematics at higher level and in fact mathematics is relative! In fact Simpson’s Paradox in Statistics and Data Analysis is also related where Statistical Data are seen in absolute sense but in reality they are relativistic in different frames of references ! The absence of relativistic reference frames in statistical analysis often could lead to paradoxes e.g. Simpson’s paradoxes having wide relevance in real-world applications.
Category: Set Theory and Logic