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By Larry Joel Goldstein

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Example text

Ist eine Nullfolge. ) eine Nullfolge. ) induziert also eine wohldefinierte Abbildung der Aquivalenzklassen rationaler Intervallschachtelungen in den Cantorschen Korper FIN der Fundamentalfolgen modulo den Nullfolgen. ) gemaB (2). ]) eine Intervallschachtelung. Wenn man § 5. Axiomatische Beschreibung der reellen Zahlen 39 anstatt von (an) von einer anderen Fundamentalfolge (a~) ausgeht, so daB (a~ - an) eine Nullfolge ist, und dazu (r~) und (s~) gemiiB (2) wiihlt, ist ([r~, s;,]) zu ([rno sn]) iiquivalent.

Rx. und /3 sind nicht leer. Jedes Element von rx. ist kleiner als jedes Element von /3. /3 hat kein kleinstes Element ("Minimum"). Jeder Schnitt ist durch seine Unter- und Obermenge je fUr sich eindeutig bestimmt. Er wird daher im folgenden mit seiner Obermenge /3 identifiziert, die folgende Eigenschaften besitzt: (0' I) (0'2) (D'3) /3 und die Komplementarmenge 71 =

Angew. Math. : Arithmetica integra, Niimberg 1544 [28] STRUWE, W. : Papyrus des staat!. Museums der schonen Kiinste in Moskau, Quellen u. : Geschichte der Elementarmathematik, Bd. 1 Arithmetik und Algebra, vollst. neu bearb. von H. Gericke, K. Reich u. K. : Lehrbuch der Algebra Bd. 1 1895, repr. der 3. Aufl. New York 1961 Kapitel 2. Reelle Zahlen K. Mainzer liyw {}' e'lvrxz alJvexic; Orrxv 'trxina yivr,'trxz Krxi iiv 'ta 'eKrx'tipOIJ rriprxc; ojc; iirrroVTrxz, Krxi roarrep ar,jlrxivez 'tOUVOjlrx, alJvixr,'trxz*) (ARISTOTELES, Physik 227a, 11-12).

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