Finite Mathematics as the Most General (Fundamental) Mathematics

The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose f...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-10, Vol.16 (10), p.1340
Main Author: Lev, Felix M.
Format: Article
Language:English
Subjects:
finite mathematics
finite quantum theory
Mathematicians
Mathematics
Numbers
Physicists
Physics
Quantum theory
standard mathematics
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Summary:The purpose of this paper is to explain at the simplest possible level why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than standard mathematics. The belief of most mathematicians and physicists that standard mathematics is the most fundamental arose for historical reasons. However, simple mathematical arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit p→∞; standard mathematics arises from finite mathematics in the degenerate case when operations modulo a number are discarded. Quantum theory based on a finite ring of characteristic p is more general than standard quantum theory because the latter is a degenerate case of the former in the formal limit p→∞.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16101340