P55 \to

Co-authored-by: Patrick Rabau <[email protected]>

spaces/S000134/properties/P000055.md

@@ -14,4 +14,4 @@ of the Euclidean metric.
 
 Assume $(x_n)$ is a Cauchy sequence not contained in a line, i.e. for
 every $n$ there exists $n'>n$ such that $x_n$ and $x_{n'}$ are not colinear with $\vec 0$.
-Then $r(x_n,x_{n'}) = d_e(x_n,\vec 0)+d_e(x_{n'},\vec 0)\geq r(x_n,\vec 0)$. The assumption $r(x_n,x_m)\to 0$ (for $n,m\to \infty$) implies $r(x_n,\vec 0)\to 0$, hence the sequence has a limit.
+Then $r(x_n,x_{n'}) = d_e(x_n,\vec 0)+d_e(x_{n'},\vec 0)\geq r(x_n,\vec 0)$. The assumption $r(x_n,x_m)\to 0$ (for $n,m\to \infty$) implies $r(x_n,\vec 0)\to 0$, hence $x_n\to\vec 0$.