According to me it is false because $F$ might be a singleton subset in $[a,b]$. If $F = \{x\}$, then it contains a constant sequence which converges to itself and hence it is closed. Length of $F, |F| = 0 $but $F$ is not empty
2026-03-25 09:29:50.1774430990
If $F$ is a closed subset of $[a,b]$ and length of $F$, $|F| = 0$ then is $F$ an empty set. True or False?
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$\{a\}$ is a subset of $[a,b]$ which is closed, but $|\{a\}|=0$.