  We show that we can approximate every function $f\in C^{k}(\bar{B_1})$ with a
$s$-harmonic function in $B_1$ that vanishes outside a compact set.
  That is, $s$-harmonic functions are dense in $C^{k}_{\rm{loc}}$. This result
is clearly in contrast with the rigidity of harmonic functions in the classical
case and can be viewed as a purely nonlocal feature.
