This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in  and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in , , , .
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[v1] 10 Mar 2010
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