Which of these statements are always true?

- A: If \( \{ a_n \} \) is
**Cauchy**sequence, then the sequence converges in any metric space - B: If \( \{ b_n \} \) bounded sequence, then it must have a sub-sequence that converges
- C: If \( \{ c_n \} \) is strictly monotonic sequence, then it converges to its infimum or supremum
- D: If \( \{ d_n \} \) is sequence that converges, every sub-sequence of \( \{ d_n \} \) converges as well
- E: If sequences \( \{ x_n \} \) and \( \{ y_n \} \), satisfy for each \( n \) : \( x_n > y_n \). Then, the following will be satisfied as well: \(\ \lim_{x\to\infty } x_n > \lim _{ y \rightarrow \infty }{ y_n } \)

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