3. Let the set
$$
A=\left\{y \left\lvert\, y=\sin \frac{k \pi}{4}(k=0, \pm 1, \pm 2, \cdots)\right.\right\} \text {. }
$$

Then the number of proper subsets of set $A$ is $\qquad$ (2009, Tongji University Independent Admission Examination)