Let $x _ { n }$ be a sequence with the following property: Every subsequence of $x _ { n }$ has a further subsequence which converges to $x$. Then the sequence $x _ { n }$ converges to $x$.
Let $x _ { n }$ be a sequence with the following property: Every subsequence of $x _ { n }$ has a further subsequence which converges to $x$. Then the sequence $x _ { n }$ converges to $x$.