good people! I am reading limit in real analysis, and stuck on a problem: If $f:[a,b]\to \Bbb R$ has a limit at every point, then $f$ is bounded.Is this true for $f:(a,b)\to \Bbb R$? Thank you.
2026-04-24 23:45:29.1777074329
limit and boundedness of a function
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No: for example $f(x) = \frac1x$ on $(0,1)$