Abstract
The main goal of this presentation is to explain that classical mathematics is a special degenerate case of finite mathematics in the formal limit p→∞, where p is the characteristic of the ring or field in finite mathematics. This statement is not philosophical but has been rigorously proved mathematically in our publications. We also describe phenomena which finite mathematics can explain but classical mathematics cannot. Classical mathematics involves limits, infinitesimals, continuity, etc., while finite mathematics involves only finite numbers.
Highlights
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
The idea of infinitesimals was in the spirit of existed experience that any macroscopic object can be divided into an arbitrarily large number of arbitrarily small parts, and, even in the 19th century, people did not know about atoms and elementary particles
The main goal of this presentation is to explain the following: Statement: Classical mathematics is a special degenerate case of finite mathematics in the formal limit p→∞, where p is the characteristic of the ring or field in finite mathematics
Summary
More than 300 years ago, Newton and Leibniz proposed the calculus of infinitesimals, and this mathematics turned out to be very successful in explaining many physical phenomena. The idea of infinitesimals was in the spirit of existed experience that any macroscopic object can be divided into an arbitrarily large number of arbitrarily small parts, and, even in the 19th century, people did not know about atoms and elementary particles. We know that when we reach the level of atoms and elementary particles standard division loses its usual meaning and in nature there are no arbitrarily small parts and no continuity. If it was possible to break the electron into parts, it would have been noticed long ago. Another example is that if we draw a line on a sheet of paper and look at this line using a microscope, we will see that the line is strongly discontinuous because it consists of atoms. The title of Weinberg’s paper [2] is “Living with infinities”
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
