Exam IV Prob 45) Given that {xn} is a bounded, divergent, infinite sequence of real numbers, which of the following must be true?

(A) {xn} contains infinitely many convergent subsequences

(B) {xn} contains convergent subsequences with different limits.

(C) {yn = min xk } is convergent. k≤n

(D) All the above

(E) (A) and (C) only

The answer is D supposedly but i don't see why for example if one considers the sequence a_n=1-1/n if n is not prime and n if n is prime then what other limit could a subsequence that is not one? My answer was E.