  Suppose we know that an object is in a sorted table and we want to determine
the index of that object. To achieve this goal we could perform a binary
search. However, suppose it is time-consuming to determine the relative
position of that object to any other objects in the table. In this scenario, we
might want to resort to an incomplete solution: we could device an algorithm
that quickly predicts the result of comparing two objects, and replace the
actual comparison with this algorithm during a binary search. The question then
is how far away are the results yielded by the imperfect binary search from the
correct answers. We present two quick lemmas that answer this question.
