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About this book
The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.
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Table of contents (23 chapters)
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Front Matter
Authors and Affiliations
Bibliographic Information
Book Title: Finite Versus Infinite
Book Subtitle: Contributions to an Eternal Dilemma
Authors: Cristian Calude, Gheorghe Păun
Series Title: Discrete Mathematics and Theoretical Computer Science
DOI: https://doi.org/10.1007/978-1-4471-0751-4
Publisher: Springer London
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London Limited 2000
Softcover ISBN: 978-1-85233-251-8Published: 25 February 2000
eBook ISBN: 978-1-4471-0751-4Published: 06 December 2012
Edition Number: 1
Number of Pages: X, 374
Topics: Mathematics, general, Mathematical Logic and Formal Languages, Artificial Intelligence, Computation by Abstract Devices