Bolzano–Weierstrass theorem
Teorema de Bolzano-Weierstrass
- Date
- 1817 (Bolzano) / c. 1865 (redescubierto por Weierstrass) · confidence medium
- Place
- Prague, Bohemia (present-day Czech Republic)
- Credited to
- Bernard Bolzano; independently rediscovered and popularized by Karl Weierstrass about fifty years later
- Field
- Knowledge & symbols
What was discovered
As an auxiliary step in his proof of the intermediate value theorem, Bolzano showed that every bounded sequence of real numbers contains a convergent subsequence. The result went unnoticed until Weierstrass independently proved it again and turned it into a central theorem of real analysis in its own right.
What it led to
- Sequential compactness in real analysis
- Rigorous foundations of topology
Built on
- Bolzano's rigorous definition of limit and continuity