1. The problem is to evaluate the expression $\sup(\{1\})$, which means finding the supremum (least upper bound) of the set containing only the number 1. 2. The supremum of a set is the smallest number that is greater than or equal to every element in the set. 3. Since the set is $\{1\}$, the only element is 1. 4. Therefore, the supremum must be 1 because 1 is the only element and is trivially the least upper bound. 5. Hence, $\sup(\{1\}) = 1$. Final answer: $\boxed{1}$