Hopf-Rinow Theorem/Corollary 2

Theorem
Let $\struct {M, g}$ be a complete connected Riemannian Manifold.

Let $\gamma$ be a minimizing geodesic segment.

Then any two points of $M$ can be joined by some $\gamma$:


 * $\forall p, q \in M : \exists \gamma : \paren {p \in \gamma} \land \paren{q \in \gamma}$