Verwandte Artikel zu Enumerability, Decidability, Computability: An Introduction...
Enumerability, Decidability, Computability: An Introduction to the Theory of Recursive Functions: 127 (Grundlehren der Mathematischen Wissenschaften) - Hardcover
Inhaltsangabe
Once we have accepted a precise replacement of the concept of algo- rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo- rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe- matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Reseña del editor
Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
- VerlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Erscheinungsdatum1969
- ISBN 10 3540045015
- ISBN 13 9783540045014
- EinbandTapa dura
- SpracheEnglisch
- Anzahl der Seiten262
- Kontakt zum HerstellerNicht verfügbar
Suchergebnisse für Enumerability, Decidability, Computability: An Introduction...
Beispielbild für diese ISBN
Enumerability, Decidability, Computability
Anbieter: Better World Books, Mishawaka, IN, USA
Verkäuferbewertung 5 von 5 Sternen
Zustand: Good. Former library book; may include library markings. Used book that is in clean, average condition without any missing pages. Bestandsnummer des Verkäufers 45242482-6
Anzahl: 1 verfügbar
Beispielbild für diese ISBN
Enumerability, Decidability, Computability: An Introduction to the Theory of Recursive Functions
ISBN 10: 3540045015
ISBN 13: 9783540045014
Gebraucht
Hardcover
Erstausgabe
Anbieter: Alien Bindings, BALTIMORE, MD, USA
Verkäuferbewertung 5 von 5 Sternen
Hardcover. Zustand: As New. No Jacket. First Edition. 1965 edition in yellow cloth. The covers look great. The spine ends are lightly indented. The binding is tight. The front flyleaf is stamped. The interior pages are clean and unmarked. Electronic delivery tracking will be issued free of charge. Bestandsnummer des Verkäufers 05016
Anzahl: 1 verfügbar
Beispielbild für diese ISBN
Enumerability Decidability Computability: An Introduction to the Theory of Recursive Functions (Grundlehren der mathematischen Wissenschaften)
Anbieter: dsmbooks, Liverpool, Vereinigtes Königreich
Verkäuferbewertung 4 von 5 Sternen
Hardcover. Zustand: Good. Good. book. Bestandsnummer des Verkäufers D8S0-3-M-3540045015-3
Anzahl: 1 verfügbar