New Infinitary Mathematics

New Infinitary Mathematics
Author :
Publisher : Charles University in Prague, Karolinum Press
Total Pages : 352
Release :
ISBN-10 : 9788024646633
ISBN-13 : 8024646633
Rating : 4/5 (633 Downloads)

Book Synopsis New Infinitary Mathematics by : Petr Vopěnka

Download or read book New Infinitary Mathematics written by Petr Vopěnka and published by Charles University in Prague, Karolinum Press. This book was released on 2022-08-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dominant current of twentieth-century mathematics, which simultaneously explores and applies infinity (albeit in bizarre ideal worlds), relies on Cantor's classical theory of infinite sets. Cantor’s theory in turn relies on the problematic assumption of the existence of the set of all natural numbers, the only justification for which – a theological justification - is usually concealed and pushed into the collective unconscious. This book begins by surveying the theological background, emergence, and development of classical set theory. The author warns us about the dangers implicit in the construction of set theory, traceable in his own and other eminent mathematicians' seminal works on the subject. He then goes on to present an argument about the absurdity of the assumption of the existence of the set of all natural numbers. However, the author’s contribution is not just a negation of current views and assumptions. On the contrary, the new infinitary mathematics that he proceeds to propose and develop is driven by a cautious effort to transcend the horizon bounding the ancient geometric world and pre-set-theoretical mathematics, whilst allowing mathematics to correspond more closely to the natural real world surrounding us. The final parts are devoted to a discussion of real numbers and to demonstrating how, within the new infinitary mathematics, calculus can be rehabilitated in its original form employing infinitesimals.


New Infinitary Mathematics Related Books

New Infinitary Mathematics
Language: en
Pages: 352
Authors: Petr Vopěnka
Categories: Mathematics
Type: BOOK - Published: 2022-08-01 - Publisher: Charles University in Prague, Karolinum Press

DOWNLOAD EBOOK

The dominant current of twentieth-century mathematics, which simultaneously explores and applies infinity (albeit in bizarre ideal worlds), relies on Cantor's c
Infinite Powers
Language: en
Pages: 389
Authors: Steven Strogatz
Categories: Biography & Autobiography
Type: BOOK - Published: 2019 - Publisher: Mariner Books

DOWNLOAD EBOOK

This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space tr
The Art of the Infinite
Language: en
Pages: 417
Authors: Robert Kaplan
Categories: Mathematics
Type: BOOK - Published: 2014-02-04 - Publisher: Bloomsbury Publishing USA

DOWNLOAD EBOOK

Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and gro
An Infinite Descent Into Pure Mathematics
Language: en
Pages:
Authors: Clive Newstead
Categories:
Type: BOOK - Published: 2019-08 - Publisher: Math Dot Coffee Publishing

DOWNLOAD EBOOK

This introductory undergraduate-level textbook covers the knowledge and skills required to study pure mathematics at an advanced level. Emphasis is placed on co
The Higher Infinite
Language: en
Pages: 555
Authors: Akihiro Kanamori
Categories: Mathematics
Type: BOOK - Published: 2008-11-23 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large card