Considering that the proposed problem allows infinite amount of questions as a valid solution then we actually do reach the sought number in the limit. Being infinitely close is the same as reaching the target as for example 1=0.9999999... by the very definition of real numbers. It would stop being true if we extended real numbers with infinitesimals, but it is not the case.
Besides, the part you quoted concerns finite precision search, which boils down to searching for a pair of intigers and those can be always found with finite amount of questions, since they are countable.