Fundamental Conceptions of Modern Mathematics (Classic Reprint) - Couverture souple

Richardson, Robert Porterfield

Couverture souple

ISBN 10 : 1440091218 ISBN 13 : 9781440091216

Editeur : Forgotten Books, 2018

Synopsis

Explore how core ideas in mathematics are defined and understood, from numbers to functions, with clear historical and conceptual context.

In this scholarly volume, readers are guided through foundational questions about what counts as a number, what makes a function, and how definitions shape mathematical practice. The text traces debates about the nature of quantity, symbols versus objects, and the language mathematicians use to describe abstract concepts. It presents critical perspectives on classic ideas, including how historical definitions and terminology evolved, and what this means for modern analysis.

With careful discussion and illustrative examples, the book helps readers see how different traditions influence the way we think about analytic truth, continuity, and the structure of functional relations. It situates these ideas within a broad view of mathematical development, inviting readers to consider how definitions affect problem solving and theory building.

• Explanations of what makes a relation analytic or non-analytic, and how continuity matters.


• Discussion of how symbols, terms, and quantities relate in counting and number theory.


• Historical perspectives on key definitions of function and their implications for practice.


• Examples that connect foundational questions to broader themes in modern mathematics.

Ideal for readers of mathematical history and philosophy who want a rigorous, accessible primer on the underpinnings of modern analysis.

A propos du livre

Présentation de l'éditeur

It is, we believe, the first attempt made on any extensive scale to examine critically the fundamental conceptions of Mathematics as embodied in the current definitions. The purpose of our examination is not solely or even chiefly to show the presence of error, but to pro mote the development of a more scientific doctrine. In expounding our own views we have often been obliged to find fault with those of others; but we have not gone out of our way for the sake of mere criticism; we have merely cleared away false doctrine preparatory to replacing it with true. Our work, though in a sense dealing with definitions, does not have as its essential scope questions as to the words to be used in expressing some thing about which there is universal agreement; it really deals with the conceptions underlying the definitions where there is, as will be shown, a great diversity of view. Further than a discussion of definitions (in this sense) we do not go, and though we have at times occasion to enunciate axioms and theorems we never set down a demonstration. It is indeed undeniable that a discipline consisting of definitions alone would be perfectly futile, but this is no argument against deeming the definitions of a science worthy of a separate exposition.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440091218
• ISBN 13: 9781440091216
• Reliure: Broché
• Nombre de pages: 244
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible