Enumerability * Decidability Computability

Name: Enumerability * Decidability Computability
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642461804
Price: 212.13 PLN
Availability: InStock

An Introduction to the Theory of Recursive Functions

Autor: Hans Hermes

Język:

Oprawa: Miękka

Wydawca: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Dostępność: Dostępna u dostawcy

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212.13 zł

Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to att...

Informacje o książce

Autor

Hans Hermes

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

2012

strony

250

EAN

9783642461804

ISBN

3642461808

Enbook ID

06960011

Wydawca

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Waga

406

Wymiary

155 x 235 x 15

Pełny opis

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.

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Enumerability * Decidability Computability

An Introduction to the Theory of Recursive Functions

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Pełny opis

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