Banach–Tarski paradox
Paradoja de Banach-Tarski
- Date
- 1924 · confidence high
- Place
- Lwów, Poland (present-day Lviv, Ukraine)
- Credited to
- Stefan Banach and Alfred Tarski
- Field
- Knowledge & symbols
What was discovered
Banach and Tarski proved that, assuming the axiom of choice, a solid ball can be decomposed into finitely many non-measurable pieces and reassembled, without distortion, into two balls identical to the original.
The Hausdorff paradox (1914) is not in the catalogue as its own entry; cited here as a direct antecedent.
What it led to
- Theory of amenable groups
- Debate over the counterintuitive consequences of the axiom of choice
- Limits on the existence of a finitely additive measure in R³