Der Ursprung Des Zahlbegriffs Book by Moritz Pasch
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Der Ursprung Des Zahlbegriffs

Der Ursprung Des Zahlbegriffs


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About the Book

Von jeher hat man es ganz besonders in der Mathematik als eine Verpflichtung empfunden, die Fachbegriffe und die zwischen ihnen sich ergebenden Beziehungen maglichst bis zu ihrem Ursprung zuriick- zuverfolgen. Wenn wir heute in der Mathematik die axiomatische Me- thode betonen, so ist diese doch dieselbe, die die Denker des Altertums anstrebten, die im Laufe der Zeit verschiittet war und im vorigen Jahr- hundert wieder belebt wurde. Die dadurch hervorgerufene Bewegung hatte zunachst die Geometrie zum Gegenstand und iibertrug sich all- mahlich auf die anderen Gebiete der Mathematik. So ist auch der Ver- fasser des vorliegenden Buches bei seinen axiomatischen Untersuchungen von der Geometrie ausgegangen, urn alsdann die dort gewonnenen Ein- sichten fiir die Analysis zu verwerten. Durch beharrlichen Ausbau der in meiner "Einleitung in die Differential- und Integralrechnung" (1882) vorbereiteten Auffassung entstanden die "Grundlagen der Analysis" (1909), sowie . die naheren Ausfiihrungen in "Veranderliche und Funk- tion" (1914). Zuerst die "Grundlagen der Analysis" (im folgenden mit GA bezeich- net): In diesen habe ich eine erste Lasung der Aufgabe, die Zahlenlehre streng axiomatisch aufzubauen, niedergelegt, einer Aufgabe, deren La- sung fiir die Geometrie den Gegenstand meines Buches "V orlesungen iiber neuere Geometrie" (1882) 1 gebildet hatte, wahrend ich den strengen Aufbau der Zahlenlehre durch die ebenfalls 1882 erschienene Einleitung in die Differential- und Integralrechnung vorbereitet hatte. In dieser wird die Lehre von den rationalen Zahlen als gegeben vorausgesetzt; aus ihr entwickle ich streng den Begriff der Irrationalzahlen und die wesentlichsten Begriffe der Infinitesimalrechnung.


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Product Details
  • ISBN-13: 9783642902260
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Binding: Paperback
  • Height: 244 mm
  • No of Pages: 50
  • Series Title: German
  • Weight: 163 gr
  • ISBN-10: 364290226X
  • Publisher Date: 01 Jan 1930
  • Edition: 1930 ed.
  • Language: German
  • Returnable: N
  • Spine Width: 3 mm
  • Width: 170 mm


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