Using the result proved for the random walk in [math]{\mathbf R}^3[/math] in Example, explain why the probability of an eventual return in [math]{\mathbf R}^n[/math] is strictly less than one, for all [math]n \ge 3[/math]. Hint: Consider a random walk in [math]{\mathbf R}^n[/math] and disregard all but the first three coordinates of the particle's position.