# Finite Versus Infinite

## Contributions to an Eternal Dilemma

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

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.

Algebra Automata Theory Cantor Finite Mathematical Logic Neural Computing Problem-solving combinatorics complexity databases function logic mathematics

- DOI https://doi.org/10.1007/978-1-4471-0751-4
- Copyright Information Springer-Verlag London 2000
- Publisher Name Springer, London
- eBook Packages Springer Book Archive
- Print ISBN 978-1-85233-251-8
- Online ISBN 978-1-4471-0751-4
- About this book