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What is the difference, if any, between $x \in {(1,3)}$ and $1

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    As far as I know, they are the same. I am not familiar with an interpretation where the endpoints "'must' be possible." – 2017-01-13

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$1 < x < 3$ and $x \in (1, 3)$ mean exactly the same thing: the open interval $(a, b)$ is by definition the set $\{x \mid a < x < b\}$ so the assertion $x \in (1, 3)$ is equivalent to the assertion $1 < x < 3$. Don't try to read too much into "elegant variations" of notation.

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    I mean, if I solve a problem and get $x \in {(1,3)}$ can I tick correct an option which says $x \in {(1,4)}$ ?Thanks. – 2017-01-13
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    Well if you got $2 < x < 3$, would $1 < x < 4$ also be correct? – 2017-01-13
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    Um, yes, but my teacher insists that while using parentheses notation we should always write the exact set. – 2017-01-13
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    I have no idea what your teacher could mean by that. It sounds like hogwash to me. – 2017-01-13