18. f:X + X is a mapping of a compact metric space X with metric p into itself, and a, and b, are any two points of X. Sequences {an} and {om} are defined by an = f(an-1), bn = f(n-1). Prove that there is an increasing sequence {kn} of positive integers such that {axn} and {bxm} are convergent. If the mapping is such that pla,b) nos plam,ao) nos plam,ao)