Inside and outside bands

For c 0, |u|>c means u<-c or u>c. For c>0, |u| <= c means -c <= u <= c. Divide out a positive multiplier first: k|u| <= c |u| <= ck, k>0. For k|u| <= |v|, square the nonnegative sides: k2u2 <= v2, then factor the difference of squares. For |u| <= v, retain v 0 as well as -v <= u <= v. For |q(x)| <= d, intersect q(x) >= -d and q(x) <= d. For |q(x)|>d, unite q(x)<-d and q(x)>d. If d<0, the first set is empty and the second is all real inputs. At d=0, distinguish zeros from nonzeros.