Observer's mathematics applications to number theory, geometry, analysis, classical and quantum mechanics

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 Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature. This work considers mathematical and physical aspects in a setting of arithmetic, algebra, geometry, and topology provided by Observer's Mathematics, see www.mathrelativity.com.