Let x[n] denote a causal sequence; i.e., x[n] = 0, n < 0. Furthermore, assume that x[0] ≠ 0.

(a) Show that there are no poles or zeros of X(z) at z = ∞, i.e., that lim _z→∞ X(z) is nonzero and finite.

(b) Show that the number of poles in the finite z-plane equals the number of zeros in the finite z-plane. (The finite z-plane excludes z = ∞.)