PDF BookThe Continuity Debate Dedekind Cantor du Bois-Reymond and Peirce on Continuity and Infinitesimals

[Read.3EPv] The Continuity Debate Dedekind Cantor du Bois-Reymond and Peirce on Continuity and Infinitesimals

[Read.3EPv] The Continuity Debate Dedekind Cantor du Bois-Reymond and Peirce on Continuity and Infinitesimals

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Book Details :
Published on: 2012-12-19
Released on:
Original language: English

The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number What, in particular, is a real number What is the true nature of continuity itself Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities Is the concept of an infinitesimally small quantity even logically coherent What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line The main question to be addressed, of course, is whether mathematical continuity exists at all. ( )-definition of limit - Wikipedia In calculus the ( )-definition of limit ("epsilondelta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis ...
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