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Transfinity: A Source Book

Wolfgang Mückenheim

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Description:Transfinity is the realm of numbers larger than every natural number: For every natural number k there are infinitely many natural numbers n > k. For a transfinite number t there is no natural number n ≥ t. We will first present the theory of actual infinity, mainly sustained by quotes, in chapter I and then transfinite set theory as far as necessary to understand the following chapters. In addition the attitude of the founder of transfinite set theory, Georg Cantor, with respect to sciences and religion (his point of departure) will be illuminated by various quotes of his as well as of his followers in chapter IV. Also the set of applications of set theory will be summarized there. All this is a prerequisite to judge the social and scientific environment and the importance of set theory. Quotes expressing a sceptical attitude against transfinity or addressing questionable points of current mathematics based on it are collected in chapter V. For a brief overview see also Kritik der transfiniten Mengenlehre or Critics of transfinity. The critique is scrutinized in chapter VI, the main part of this source book. It contains over 100 arguments against actual infinity – from doubtful aspects to clear contradictions – among others applying the newly devised powerful method of ArithmoGeometry. Finally we will present in chapter VII a theory, MatheRealism, that shows that in real mathematics, consisting of monologue, dialogue, and discourse between real thinking-devices, via necessarily physical means, infinite sets cannot exist other than as names. This recognition removes transfinity together with all its problems from mathematics – although the application of mathematics based on MatheRealism would raise a lot of technical problems.Page numbers of subsections in chapters V and VI have not been listed because these chapters are continuously extended. All subsections can easily be found by their headings.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Transfinity: A Source Book. To get started finding Transfinity: A Source Book, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 365

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: 2021

ISBN

Description: Transfinity is the realm of numbers larger than every natural number: For every natural number k there are infinitely many natural numbers n > k. For a transfinite number t there is no natural number n ≥ t. We will first present the theory of actual infinity, mainly sustained by quotes, in chapter I and then transfinite set theory as far as necessary to understand the following chapters. In addition the attitude of the founder of transfinite set theory, Georg Cantor, with respect to sciences and religion (his point of departure) will be illuminated by various quotes of his as well as of his followers in chapter IV. Also the set of applications of set theory will be summarized there. All this is a prerequisite to judge the social and scientific environment and the importance of set theory. Quotes expressing a sceptical attitude against transfinity or addressing questionable points of current mathematics based on it are collected in chapter V. For a brief overview see also Kritik der transfiniten Mengenlehre or Critics of transfinity. The critique is scrutinized in chapter VI, the main part of this source book. It contains over 100 arguments against actual infinity – from doubtful aspects to clear contradictions – among others applying the newly devised powerful method of ArithmoGeometry. Finally we will present in chapter VII a theory, MatheRealism, that shows that in real mathematics, consisting of monologue, dialogue, and discourse between real thinking-devices, via necessarily physical means, infinite sets cannot exist other than as names. This recognition removes transfinity together with all its problems from mathematics – although the application of mathematics based on MatheRealism would raise a lot of technical problems.Page numbers of subsections in chapters V and VI have not been listed because these chapters are continuously extended. All subsections can easily be found by their headings.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Transfinity: A Source Book. To get started finding Transfinity: A Source Book, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Transfinity: A Source Book

Transfinity: A Source Book

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