Zusammenfassung
Es sind nicht alle Zahlen gleich vor dem Herrn. Die reellen Zahlen entsprechen zwar Punkten auf der Zahlengeraden und ähneln in diesem Sinne einander, aber es gibt dennoch gewaltige Unterschiede zwischen ihnen. Einige von ihnen wurden von den Frühmenschen geschaffen (1,2,3), andere von den kultivierten Griechen (√2, π) und wieder andere von den Entdeckern der Differential- und Integralrechnung (e). Über die elementare Unterscheidung zwischen ganzen und nichtganzen Zahlen hinaus gibt es die Einteilungen in rationale und irrationale Zahlen oder in algebraische und transzendente Zahlen. Moderneren Ursprungs sind andere Eigenschaften gewisser — aber nicht aller — reeller Zahlen wie z.B. Normalität und Berechenbarkeit in Echtzeit. In diesem Kapitel stellen wir einige ungelöste Probleme zu Eigenschaften einiger berühmter Zahlen vor und werden unterwegs einigen interessanten, aber weniger bekannten Zahlen begegnen, wie zum Beispiel der Champernowneschen Zahl (0,12345678910111213...) und der Liouvilleschen Zahl (0,1100010000000000000001000...).
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Klee, V., Wagon, S. (1997). Interessante reelle Zahlen. In: Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6073-4_3
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