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|Title:||The new digital mathematics of the millennium||Authors:||Kyritsis, Konstantinos||Keywords:||Mathematics;Calculus||Issue Date:||20-Feb-2019||Abstract:||This project is under the next philosophical principles 1) Consciousness has the experience of the infinite. 2) But the physical material world is finite. 3) Therefore mathematical models in their ontology should contain only finite entities and should not involve the infinite at all which is a phenomenological abstraction. In digital mathematics we may have the concepts of seemingly infinite sets (or seemingly infinitesimal numbers) but they are essentially finite sets or numbers with finite decimal representation. These principles allow for an alternative and more realistic universe of mathematics, directly usable in artificial intelligence of computers. The development of digital mathematics is somehow more elaborate in the definitions but radically easier in the proofs compared to classical mathematics. It is certainly not equivalent to the classical mathematics. But here we give emphasis only to the theorems that are very similar and very familiar with corresponding to classical mathematics. The previous principles require a rewriting of the classical axiomatic systems to those of 1) the natural digital numbers, 2) the digital 1st and 2nd order formal logic, 3) the digital set theory, 4) the digital real numbers, 5) the digital differential and integral calculus, 6) the digital Euclidean axiomatic continuous geometry etc. In the next two papers we present the digital real numbers with the digital differential and integral calculus and the digital axiomatic continuous Euclidean geometry, where all sets of points (visible or invisible) or numbers are finite sets of points and numbers with finite decimal representation. Our perception and experience of the reality, depends on the system of beliefs that we have. In mathematics, the system of spiritual beliefs is nothing else than the axioms of the axiomatic systems that we accept. The rest is the work of reasoning and acting. For each of the two papers we give at its end a fictional philosophical or epistemological dialogue with the celebrated immortals of the classical mathematics (like Euclid, Pythagoras, Hilbert, Cantor, Gödel, Newton, Leibniz etc) where the reader can grasp in non-technical terns the main differences and the main advantages (or disadvantages) of the digital mathematics where all are finite compared to the classical mathematics which are based on the phenomenological abstraction of the infinite The 2nd of the two papers on the digital but continuous axiomatic Euclidean geometry has already been published in the World Journal of Research and Review (WJRR)ISSN:2455-3956, Volume-5, Issue-4, October 2017 Pages 31-43||URI:||http://cris.teiep.gr/jspui/handle/123456789/1684|
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