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Isodimensional Discrete Mathematics (IDM)

The IDM isa different mathematics,thanks to the discrete nature of its foundations. The definition of basic mathematical concepts(numbers, number systems, real line,etc.) is simpler and more intuitive, without diminishing mathematical rigor. In addition,discrete foundationsusually simplifies reasonings and proofs and, in general, facilitates mathematical abstraction. Another IDM quality to highlight is thatit does not interfere at all with the principles, criteria, and/or approaches of traditional mathematicsbecause, simply, they are two different ways of doing math, but sharing the same mathematical concepts. So, the conclusions obtained in one of them can be valid in the other, and vice versa. The IDM foundations are in the bookNuevos Fundamentos de la Recta Numérica, which can be downloaded freely. It is also available in paper (soft cover), both in Spanish and in English(Discrete Foundations of Real Numbers).This book is self-sufficient in its content, but it is an extract of another much more voluminous entitledFundamentos Discretos de una Nueva Matemática,devotedto the study of basic concepts of different types(arithmetic, algebraic, geometric, etc.), from the perspective of discrete foundations. This analysishas allowed us to solve some pending questions in traditional mathematics, such as unifying circular and hyperbolic complex numbers, or providing working methods that are not viable (in a general form) incontinuous mathematics, such as the differentiation and integration of discrete functions. Other topics of interest are also dealt with, for example, finding out thereasons for some basic theorems, or knowing thenature of the main mathematical constants, oranalyzing complex and hyper-complex algebras(which exceed one million, so only statistical results on its properties are provided), orstudying basic physical concepts(randomness, time, entropy,etc.) from the point of view of the IDM. More details about this book can be found in the table of contents.