Die naturlichen Grundlagen der Mathematik

by Helmut Bender

Book cover: Die naturlichen Grundlagen der Mathematik

Extent: 97 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: German

Paperback (Published)

(September 2015)

ISBN: 9783832540722

6.65 x 9.45 inches

Price: $26.00

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Dieses Buch ist als eine Neubegrundung der Mathematik zu verstehen. Mathematische Grundkenntnisse genugen zum Verstandnis. In logischer Hinsicht wird nur der vertraute Umgang mit den Worten und, oder, wenn ,/ ,dann vorausgesetzt. Logische Fachkenntnisse sind somit nicht notig, eher hinderlich. Die Grundbegriffe Objekt, Bereich, Abbildung sind rein sprachlicher Natur: Ein Bereich erlaubt, von seinen Elementen (Objekte) zu reden, eine Abbildung alpha von dem “Bild” x alpha(ein Objekt) eines Objektes x. Und selbstverstandlich sind Bereiche wie Abbildungen auch Objekte. Einhergehend mit Negation wird Existenz eingefuhrt, Gleichheit dann im Zusammenhang mit dem Begriff einer Klasse (Bereich plus Aquivalenzrelation), und schliesslich wird die Klasse aller Mengen vorausgesetzt. Das Standard-Vorlesungsthema Aufbau des Zahlensystems wird zunachst auf althergebrachter Grundlage behandelt (Mengen und Abbildungen im Sinne Dedekinds), in dem vertrauten Rahmen der real existierenden Mathematik. Der entsprechende, um einiges angereicherte Teil I des Buches ist daher von unabhangigem Interesse, wie auch Teil II mit historischen und mathematikphilosophischen Erorterungen.

  • By (author) Helmut Bender

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