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Bernard BolzanoHis Life and Work$
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Paul Rusnock and Jan Sebestík

Print publication date: 2019

Print ISBN-13: 9780198823681

Published to Oxford Scholarship Online: June 2019

DOI: 10.1093/oso/9780198823681.001.0001

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(p.502) Chapter 9 Mathematics
Bernard Bolzano

Paul Rusnock

Jan Šebestík

Oxford University Press

This chapter presents an overview of Bolzano’s work in mathematics and its philosophy, while presenting some interesting samples of his work. It begins with a discussion of his views on mathematical method in their historical context, followed by an exposition of some of his best work in real analysis. In particular, the chapter discusses his early work on infinite series and his analysis of continuity, beginning with the Purely Analytic Proof (1817), and extending to his construction of a continuous, nowhere differentiable function in the 1830s, called Bolzano’s function.

Keywords:   foundations, analysis, infinite, continuity, proof, definition, mathematical method, Bolzano’s function

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