The Mathematics of Infinity

A Guide to Great Ideas

Theodore G. Faticoni

288 pages, parution le 25/07/2006

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Résumé

A balanced and clearly explained treatment of infinity in mathematics.

The concept of infinity has fascinated and confused mankind for centuries with concepts and ideas that cause even seasoned mathematicians to wonder. For instance, the idea that a set is infinite if it is not a finite set is an elementary concept that jolts our common sense and imagination. the Mathematics of Infinity: A guide to Great Ideas uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing.

Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world.

With a thoughtful and balanced treatment of both concepts and theory, The Mathematics of Infinity focuses on the following topics:

Sets and Functions
Images and Preimages of Functions
Hilbert's Infinite Hotel
Cardinals and Ordinals
The Arithmetic of Cardinals and Ordinals
the Continuum Hypothesis
Elementary Number Theory
The Riemann Hypothesis
The Logic of Paradoxes

Recommended as recreational reading for the mathematically inquisitive or as supplemental reading for curious college students, the Mathematics of Infinity: A Guide to Great Ideas gently leads readers into the world of counterintuitive mathematics.

Sommaire

Elementary Set Theory
Functions
Counting Infinite Sets
Infinite Cardinals
Well Ordered Sets
Inductions and Numbers
Prime Numbers
Logic and Meta-Mathematics

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Theodore G. Faticoni
Parution	25/07/2006
Nb. de pages	288
Format	16 x 24
Couverture	Relié
Poids	542g
Intérieur	Noir et Blanc
EAN13	9780471794325
ISBN13	978-0-471-79432-5