For some [[../02 Areas/Math/Linear Transformation|Linear Map]] $T$: Suppose that $T$ is [[../02 Areas/Math/Injective|one-to-one]], $ \begin{align} \let x \neq y &\in \R^n \\ T(\vec x) - T(\vec y) &= T(\vec x - \vec y) \neq \vec 0 \\ \vec x - \vec y &\neq \vec{0} \\ T(\vec x) &\neq T(\vec y) \end{align} $