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If you know that m < n, you can use x∈(m, n), but I find it's relatively common when working with abstract functions to know that x must be between two values, but not know which of those values is larger.
For example, with the intermediate value theorem, a continuous function f over [a, b] has the property that for every y between f(a) and f(b), ∃ x ∈ [a, b] : f(x) = y.
It would be nice if there were some notation like \f(a), f(b)/ or something which could replace that big long sentence with just ∀ y ∈ \f(a), f(b)/ without being sensitive to which argument is larger.
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