Let a and b be two scalars and a is less than b, prove that for any sequence in $[a,b]$ there must be a subsequence converging to some point in $[a,b]$
2026-03-25 02:57:57.1774407477
Prove must exist subsequence converges
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What if $a = 0, b = 1$, and the sequence is $1/n$? This sequence converges to $0$, which is not in $(0,1)$. The reason is that you need to consider the closed interval $[a,b]$. Then the result follows from compactness (see this).