Discussion of foundation of mathematics and quantum theory

Abstract

Following the results of our recently published book [F. Lev, Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory. With Applications to Gravity and Particle Theory, Springer, 2020, ISBN 978-3-030-61101-9], we discuss different aspects of classical and finite mathematics and explain why finite mathematics based on a finite ring of characteristic pp is more general (fundamental) than classical mathematics: the former does not have foundational problems, and the latter is a special degenerate case of the former in the formal limit p→∞p\to \infty . In particular, quantum theory based on a finite ring of characteristic pp is more general than standard quantum theory because the latter is a special degenerate case of the former in the formal limit p→∞p\to \infty .

Keywords

• finite mathematics
• classical mathematics
• finite quantum theory
• 03a05
• 11axx
• 11txx
• 13mxx
• 16gxx
• 81r05