Rigorous analysis: limits, continuity, epsilon-delta
Rigorización del análisis: límites, continuidad y definición epsilon-delta
- Date
- 1817-1821 · confidence high
- Place
- Paris (École Polytechnique) and Prague
- Credited to
- Bernard Bolzano (1817), Augustin-Louis Cauchy (Cours d'analyse, 1821), Karl Weierstrass (1860s)
- People
- 👤 Augustin Louis Cauchy1789–1857👤 Bernard Bolzano1781–1848👤 Karl Weierstraß1815–1897
- Field
- Knowledge & symbols
What was discovered
The definition of limit and continuity without infinitesimals, the intermediate value theorem, the Cauchy convergence criterion and, with Weierstrass, the epsilon-delta formulation and the continuous function with no derivative anywhere. It put calculus on solid foundations.
Bolzano's work in Prague went almost unnoticed; Weierstrass's Berlin school completed the arithmetisation.
What it led to
- the construction of the real numbers
- function theory
- topology
- functional analysis
Built on
- Fourier series and transform1807
- Newton and Leibniz's calculus
- Fourier series