Cauchy's conception of rigour in analysis (Q1079555)

The author surveys various features of Cauchy's creation of real-variable analysis between 1814 and 1824; some of his views on complex numbers are also recalled, although the theory of functions of a complex variable and the associated residue calculus are not rehearsed. The topics covered include: Cauchy's forms of proof; continuous and discontinuous functions; evaluation of definite integrals, including by use of i; infinite single integrals and double integrals; and the refutation of Lagrange's approach to the calculus. In a note added in proof the author rejects the recent claim by \textit{E. Giusti} [see Boll. Stor. Sci. Mat. 4, No. 2, 24--54 (1984; Zbl 0573.01004)] that Cauchy's analysis can be ``saved'' by interpreting convergence as uniform convergence.