Intermediate value theorem
Teorema del valor intermedio
- Date
- 1817 · confidence high
- Place
- Prague, Bohemia (present-day Czech Republic)
- Credited to
- Bernard Bolzano
- Field
- Knowledge & symbols
What was discovered
Bolzano rigorously proved that a continuous function that changes sign at the endpoints of an interval must vanish somewhere inside it, using for the first time a formal definition of continuity based on inequalities. Cauchy published an independent proof in 1821 that popularized the result.
Cauchy published an independent proof in 1821 that spread the result; earlier, Simon Stevin had used similar ideas for polynomial roots, without a general proof.
What it led to
- Rigorous foundations of mathematical analysis
- Bolzano–Weierstrass theorem
Built on
- Newton and Leibniz's infinitesimal calculus