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Pankaj Mani - One of the best experts on this subject based on the ideXlab platform.

  • godel incompleteness results cantor diagonalization countability of real numbers famous paradoxes e g richard russell skolem liar set theory zfc in relativistic Mathematical Space time
    viXra, 2020
    Co-Authors: Pankaj Mani
    Abstract:

    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 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 framework. This could possibly lead to entirely new way of looking at conventional mathematics in broader sense.

Edgar E. Escultura - One of the best experts on this subject based on the ideXlab platform.

  • the new real number system and discrete computation and calculus
    Neural Parallel & Scientific Computations archive, 2009
    Co-Authors: Edgar E. Escultura
    Abstract:

    The paper points out the inconsistency and ambiguity of the field axioms of the real number system and notes that the only clearly defined and consistent Mathematical model of the real numbers is the set of terminating decimal. Then it identifies present mathematics having global applications. They are continuous and discrete; the former meets the needs of the natural sciences since physical Space is a continuum that pervades everything in nature and the latter of computing and applications since physical systems are discrete. Then the base Mathematical Space over which mathematics is to be built called the new real number system is developed using three consistent axioms. This new Mathematical Space is a continuum, non-Archimedean and non-Hausdorff but contains the subSpace of decimals which is discrete, Archimedean and Hausdorff. It introduces a new norm that has many advantages over the other norms of the real number system, especially, for purposes of computing.

Roger B Nelsen - One of the best experts on this subject based on the ideXlab platform.

Amrit Sorli - One of the best experts on this subject based on the ideXlab platform.

  • Mathematical Space time neuronal Space time and timeless quantum Space
    viXra, 2009
    Co-Authors: Amrit Sorli
    Abstract:

    The universe is in a continuous change. A change n gets transformed into a change n+1, the change n+1 into a change n+2 and so on. Clocks measure a frequency, velocity and numerical order of change. Experimental date confirms that changes and clocks do not run time; they run in quantum Space only. Time is not a part of quantum Space. Quantum Space itself is timeless. Physical time that is clocks run is man created physical reality. Space-time is a math model merely. Fundamental arena of the universe is timeless quantum Space. In the timeless quantum Space into which massive bodies and elementary particles move there is no past and no future. Past and future belong to the inner neuronal Space-time that is a result of neuronal activity of the brain.

Claudi Alsina - One of the best experts on this subject based on the ideXlab platform.