Finite mathematics as the most general (fundamental) mathematics - Archive ouverte HAL
Article Dans Une Revue Symmetry Année : 2024

Finite mathematics as the most general (fundamental) mathematics

Felix Lev
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Résumé

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 → ∞.
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Dates et versions

hal-04731499 , version 1 (10-10-2024)

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Felix Lev. Finite mathematics as the most general (fundamental) mathematics. Symmetry, 2024, Symmetry, 16 (10), paper 1340. ⟨10.3390/sym16101340⟩. ⟨hal-04731499⟩
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