Finite mathematics as the most general (fundamental) mathematics

• URL: http://arxiv.org/abs/2203.09482v2
• Date: Tue, 20 Aug 2024 19:27:55 GMT
• Title: Finite mathematics as the most general (fundamental) mathematics
• Authors: Felix M Lev,
• Abstract summary: 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 $ptoinfty$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 {\it mathematical} arguments show that standard mathematics (involving the concept of infinities) is a degenerate case of finite mathematics in the formal limit $p\to\infty$: 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 $p\to\infty$.

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