# Statement(s)
> [!NOTE] Statement 1 (Translation Invariance of Euclidean Metric)
> For all $x,y,z \in \mathbb{R}^m$ we have $d(x,y)= d(x-z, y-z)$
# Proof(s)
**Proof of statement 1:** $d(x,y)=\lvert \lvert x-y \rvert \lvert = \lvert\lvert (x-z) -(y-z)\rvert \rvert = d(x-z, y-z) $ $\blacksquare$
**Proof 2.** ... $\blacksquare$
# Application(s)
**Consequences**:
**Examples**:
# Bibliography