Alternately, if x ^ ^ and p ^ ^ were bounded operators, note that [ x ^ ^ n , p ^ ^ ] = i ℏ ℏ n x ^ ^ n − − 1 , hence the operator norms would satisfy 2 ‖ p ^ ^ ‖ ‖ x ^ ^ n − − 1 ‖ ‖ x ^ ^ ‖ ≥ ≥ n ℏ ℏ ‖ x ^ ^ n − − 1 ‖ , so that, for any n, 2 ‖ p ^ ^ ‖ ‖ x ^ ^ ‖ ≥ ≥ n ℏ ℏ However, n can be arbitrarily large, so at least one operator cannot be bounded, and the dimension of the underlying Hilbert space cannot be finite. If the operators satisfy the Weyl relations (an exponentiated version of the canonical commutation relations, described below) then as a consequence of the Stone–von Neumann theorem, both operators must be unbounded.