Brownian motion

Show that the total variation of a standard Wiener process over any non-trivial interval does not exist. [The total variation $V_{a, b}(f)$ of a function $f: \mathbb {R} \rightarrow \mathbb {R}$ over the bounded interval $[a, b]$ is defined as

where the supremum is taken over all increasing sequences $s_{0} = a, s_{1}, s_{2}, \ldots , s_{n} = b$. You may find it useful that the quadratic variation of the Wiener process exists and is non-zero almost surely.]