Solution
= Solution
If $f$ is a <strictly increasing function> and $x\ne y$, one of $x<y$ or $y<x$ holds. The corresponding strict inequality of function values shows that $f$ is <injective>. Conversely, if $f(x)<f(y)$, then $x=y$ is impossible and $x>y$ would imply $f(x)>f(y)$. Thus
$$
\boxed{f(x)<f(y)\ \Longrightarrow\ x<y.}
$$
Together with strict increase, this says that such a function preserves and reflects the ordering of points.