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Georg Cantor
Paperback
Series: Biographien Hervorragender Naturwissenschaftler, Techniker U, Book 79
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ISBN10: 3322007006
ISBN13: 9783322007001
Publisher: Vieweg+teubner Verlag
Published: Jan 1 1985
Pages: 135
Weight: 0.32
Height: 0.30 Width: 5.00 Depth: 8.00
Language: German
ISBN13: 9783322007001
Publisher: Vieweg+teubner Verlag
Published: Jan 1 1985
Pages: 135
Weight: 0.32
Height: 0.30 Width: 5.00 Depth: 8.00
Language: German
Das Uncndlichc .hat wic kcine andere Fragc yon jchcr so tid das Gem i.i t der Menschcn bcwegt; (bs Uncndliche hat wie kaum cine andere Ide e auf den Verstand so anregcnd unci fruchtbar gewirkt; das Uncncllichc ist aber auch wie kcin andcrcr Beg r iff so der Auf k 1 'i. run g bediirftig. Hilbert [104. S. 163] 100 Jahre sind vcrgangcn, seit in den Mathcmatischen Annalen der scchste und letztc Teil von Cantors fundamentaler Arbeit, . Dber unendliche lineare Punktmannigfaltigkeiten erschienen ist. Damit war die Mengenlehre geboren und mit ihr eine prinzipiell neue Auffassung des Unendlichen in der Mathematik, verk6rpert in Cantors Theorie der transfiniten Zahlen. Diese Theorie hat Hilbert als die bewundernswerteste Bliite mathcmatischcn Gcistes und iiberhaupt eine der hochsten Leistungen rein verstandcsma/)i- ger menschlicher Tatigkeit bezeichnet. Anfangs unbeachtet oder abgelehnt, zu Ende des vorigen Jahr- hunderts zunehmend anerkannt und verwendet, durch die Ent- deckung der Antinomien erneut erschiittert, ist die Mengenlchre in ihrer heutigen axiomatisierten Gestalt eines der Fundamente der Mathematik. Die Tatsache, daB aile mathematischen Bcgriffc auf mengentheoretische Begriffe zuriickgefiihrt werden k6nnen, hat einige Autorcn sogar zu der Bchauptung veranlaBt, die gc- samte Mathematik sei letztlich mit der Mengenlehre identisch.
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