Editing Turing reduction (section)

== The use of a reduction ==

Since every reduction from a set <math>A</math> to a set <math>B</math> has to determine whether a single element is in <math>A</math> in only finitely many steps, it can only make finitely many queries of membership in the set <math>B</math>. When the amount of information about the set <math>B</math> used to compute a single bit of <math>A</math> is discussed, this is made precise by the ''use'' function. Formally, the ''use'' of a reduction is the function that sends each natural number <math>n</math> to the largest natural number <math>m</math> whose membership in the set <math>B</math> was queried by the reduction while determining the membership of <math>n</math> in <math>A</math>.