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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 01 July 2022

Mathematics

Mathematics

Chapter:
(p.502) Chapter 9 Mathematics
Source:
Bernard Bolzano
Author(s):

Paul Rusnock

Jan Šebestík

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198823681.003.0010

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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