# Theory check

Calculus Level 4

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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