N atur non facit saltus? This ebook is dedicated to the basic challenge which arises contin uously within the technique of the human research of fact: the position of a mathematical gear in an outline of fact. We pay our major recognition to the function of quantity platforms that are used, or can be utilized, during this procedure. we will exhibit that the image of truth in accordance with the normal (since the works of Galileo and Newton) equipment of genuine research isn't the detailed real way of featuring truth in a human mind. There exist different photographs of fact the place different num ber fields are used as simple components of a mathematical description. during this publication we attempt to construct a p-adic photograph of fact according to the fields of p-adic numbers Qp and corresponding research (a specific case of so referred to as non-Archimedean analysis). despite the fact that, this ebook must never be regarded as just a e-book on p-adic research and its functions. We learn a way more prolonged diversity of difficulties. Our philosophical and actual rules might be learned in different mathematical frameworks which aren't obliged to be in accordance with p-adic research. we will convey that many difficulties of the outline of fact as a result of actual numbers are prompted by way of limitless functions of the so known as Archimedean axiom.
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