Abstract
When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newtonʼs definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observerʼs Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.
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