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Graduate Proving two convergent subsequences have different limits when sequence is non-convergent
I am trying to prove a question : Assume K\inR^{m} is compact and {xn} (n from 1 to infinite) is a sequence of points in K that does not converge . Prove that there are 2 subsequences that converge to different points in K . Hint : Let yi=x_{ni} be one subsequence that converges to a point in...