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Let $f:I\rightarrow R$ be a monotonically increasing function on an open interval.If the image of this interval is an interval then would $f$ be continuous? For the case when $f(I)$ is open then I can deduct continuity of $f$.But What if $f(I)$ closed?

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    When you say *monotonically increasing*, do you mean that $x implies that $f(x) ($f$ is strictly increasing), or do you mean that $x\le y$ implies that $f(x)\le f(y)$ ($f$ is non-decreasing)?2012-11-29
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    The latter case.2012-11-29
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    I thought that that was probably the case, since $f[I]$ couldn’t be a closed interval otherwise, but I wanted to make sure, even though it doesn’t actually affect the argument.2012-11-29

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