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Does there exist an elementary function on some subset $I$ of $R$ such that you can prove that $A = \{\sup(f(x)): x \in I\}$ exists, but you cannot find the value of $A$ ?

If the answer is "no", then replace "elementary function" above by "function" as a further question

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    I guess the answer is no, because you can probably always use some computer programme to split the range into intervals of 2, then 4, then 8, and and so on, narrowing down the supremum or infimum to desired accuracy.2012-11-13

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