Encyclopedic dictionary of mathematics (2nd ed.)
Encyclopedic dictionary of mathematics (2nd ed.)
The flux theory of gravitation XVII: the new mathematics and physics
Applied Mathematics and Computation
Continuity and change (activity) are fundamentally related in DEVS simulation of continuous systems
AIS'04 Proceedings of the 13th international conference on AI, Simulation, and Planning in High Autonomy Systems
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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.