>>14170790Ok, I admit that the initial post is of low quality, let me elaborate the question at hand in detail.
The supremum is, as we all know, the least upper bound. The infimum is conversely the largest lower bound. For all nonempty subsets (let us say the extended reals so sup/inf will always exist) one has the intuitive result, that the supremum is larger than the infimum. However the supremum of the empty set is (defined?) to be -infinity and the infimum takes +infinity.
If the values +-infinity are weird, we can also take the bounded set [-5,7] and look at the supremum of the empty set there.
