Which of the following statements is FALSE?
1
If a sequence X of real numbers converges to a real number and has two convergent subsequences X' and X" whose limits are not equal, then X is divergent.
2
A Cauchy sequence of real numbers is unbounded.
3
If a sequence (xn) of real number converges to a real number x, then any subsequence (xnK) of (xn) also converges to x.
4
A bounded sequence of real numbers has a convergent subsequence.