Book:Thomas J. Jech/The Axiom of Choice/Errata

Errata for 1973: Thomas J. Jech: The Axiom of Choice

Banach-Tarski Paradox: Proof

$1.3$ A paradoxical decomposition of the sphere: Proof of Theorem $1.2$

Now, it is easy to find some rotation $\alpha$ (not in $G$) such that $Q$ and $Q \cdot \alpha$ are disjoint, and so, using

$\overline C \approx \overline A \cup \overline B \cup \overline C$,

there exists $S \subset C$ such that $\overline S \approx \overline Q$. Let $p$ be some point in $\overline S - \overline C$. Obviously, $\ldots$