  Let S(n,k) denote the Stirling numbers of the second kind. We prove that the
p-adic limit of S(p^e a + c, p^e b + d) as e goes to infinity exists for all
integers a, b, c, and d. We call the limiting p-adic integer S(p^\infty a + c,
p^\infty b + d). When a equiv b mod (p-1) or d \le 0, we express them in terms
of p-adic binomial coefficients introduced in a recent paper.
