It is sometimes said that the universe is homogeneous and isotropic. What is meant by each of these descriptions? Are they mutually exclusive, or does one require the other? And what implications rise because of this?


Question: Is it possible to have a convergent subsequence of a divergent sequence?
Answer: It depends on your definition of divergence:  If you mean non-convergent, then the answer is yes; If you mean that the sequence "goes to infinity", than the answer is no.