 The definition of "q""i" causes a single binary digit to go from 0 to 1 each time "i" increases by 1.Thus there will be some "n" where a large enough initial segment of "x" has already been determined by "q""n" that no additional binary digits in that segment could ever be turned on, which leads to an estimate on the distance between "q""i" and "q""j" for "i","j" > "n".If any such a function "r" were computable, it would lead to a decision procedure for "A", as follows.