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Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.
A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra. The Elements of Cantor Sets provides coverage of: Basic definitions and background theorems as well as comprehensive mathematical details A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, p-adic numbers, and several generalizations of Cantor Sets A wide spectrum of topics from measure theory to the Monty Hall Problem An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses within mathematics, computer science, engineering, and physics departments, The Elements of Cantor Sets is also appropriate as a useful reference for researchers and secondary mathematics education majors.
This book is the essential pastoral resource to help you prepare the liturgy each day of the liturgical year! If you are a priest or deacon, liturgist, music director, worship team member, religious educator, or simply interested in more information about Catholic liturgy, this publication will be an invaluable tool
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
First Published in 2001. Routledge is an imprint of Taylor & Francis, an informa company.
Sing to the Lord: Music in Divine Worship provides basic guidelines for understanding the role and ministry of music in the liturgy. An excellent resource for priests, deacons, and music ministers!
THE HIGHLY ANTICIPATED SECOND NOVEL FROM THE WRITER EMILY ST. JOHN MANDEL (STATION ELEVEN) CALLS “SHARP, WITTY, AND IMMENSELY ENTERTAINING” Is a new life possible? Because Shira Greene’s life hasn’t quite turned out as planned. She’s a single mom living with her daughter and her gay friend, Ahmad. Her PhD on Dante’s Vita Nuova hasn’t gotten her a job, and her career as a translator hasn’t exactly taken off either. But then she gets a call from a Nobel Prize-winning Italian poet who insists she’s the only one who can translate his newest book. Stunned, Shira realizes that—just like that— her life can change. She sees a new beginning beckoning: academic glory, demand for her translations, and even love (her good luck has made her feel more open to the entreaties of a neighborhood indie bookstore owner). There’s only one problem: It all hinges on the translation, and as Shira starts working on the exquisitely intricate passages of the poet’s book, she realizes that it may in fact be, well ... impossible to translate. A deft, funny, and big-hearted novel about second chances, Good on Paper is a grand novel of family, friendship, and possibility.
Widely regarded as the authoritative reference in the field, this volume comprehensively reviews theory and research on the self. Leading investigators address this essential construct at multiple levels of analysis, from neural pathways to complex social and cultural dynamics. Coverage includes how individuals gain self-awareness, agency, and a sense of identity; self-related motivation and emotion; the role of the self in interpersonal behavior; and self-development across evolutionary time and the lifespan. Connections between self-processes and psychological problems are also addressed. New to This Edition *Incorporates significant theoretical and empirical advances. *Nine entirely new chapters. *Coverage of the social and cognitive neuroscience of self-processes; self-regulation and health; self and emotion; and hypoegoic states, such as mindfulness.