Analysis l by Vladimir A. Zorich

By Vladimir A. Zorich

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Deswegen legen wir besonderen Wert auf ihre Eigenschaft der Vollstandigkeit oder Kontinuitat, die den Keim zur Idee fiir den Ubergang zu Grenzwerten - die zentrale nicht arithmetische Operation der Analysis - enthalt. 1 D e f i n i t i o n d e r M e n g e d e r r e e l l e n Z a h l e n D e f i n i t i o n 1. Eine Menge M wird als Menge der reellen Zahlen bezeichnet und ihre Elemente sind reelle Zahlen, wenn die folgenden Bedingungen, die das Axiomensystem der reellen Zahlen genannt werden, erfiillt sind.

Wie die Logiker sagen wiirden, ist das Axiomensystem kategorisch? Hierbei muss Eindeutigkeit folgendermafien verstanden werden. , fix + y) = f{x)+fiy), fix • y) = fix) • fiy) , x

Dieses Beispiel zeigt wiederum, dass die formale Schreibweise einer Aussage verglichen niit einer verbalen Formulierung bei weitem nicht inimer die kiirzeste und iibersichtlichste ist. Da wir dies beriicksichtigen, werden wir zukiinftig logischen Symbolismus nur soweit benutzen, wie uns fiir eine groflere Kompaktheit oder Klarheit in der Formulierung sinnvoU ersclieint. 5. Sei / : X —>• Y eine Abbildung. Formulieren Sie die logisclie Negierung jeder der folgenden Aussagen: a) / ist surjektiv, b) / ist injektiv, c) / ist bijektiv.

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