Show that $W_t$ is almost surely non-differentiable at $t=0$. Of course, $W(t)$ denotes a standard Wiener process.
It is enough to show that
$$P(\{\omega : \exists \epsilon>0 \: \forall \delta >0 \:\exists t<\delta :\frac{|W_t(\omega)|}{|t|} >\epsilon\})=1 \mbox{.}$$
Any hint please?