Bolzano's inheritance research in Bohemia (Q2767836)

The author analyzes the publication, history and contents of Bolzano's work, arguing that Bolzano went beyond even Cauchy in the rigorization and arithmetization of analysis. Like Dedekind and others, Bolzano had the idea that real numbers should be defined as sets of rational numbers. For Bolzano a real number (measurable expression) was any object \(S\) such that for each positive integer \(q\) there is an integer \(p\) such that \(\frac pq\leq S< \frac{p+1}q\). A positive infinitesimal was a measurable expression such that \(p=0\) for all \(q\). Historians have argued over the correct interpretation of Bolzano's rather cryptic exposition of this subject, leading to a debate that the author discusses in some detail. Finally, in the last section, the author argues that Cauchy and Bolzano actually met face to face in Prague in 1834 or 1835.NEWLINENEWLINEFor the entire collection see [Zbl 0976.00021].