1. AlgebraIn mathematics, a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values (its image) is bounded. In other words, there exists a real number M {\displaystyle M} such that | f ( x ) | ≤ M {\displaystyle |f(x)|\leq M} for all x {\displaystyle x} in X {\displaystyle X} . A function that is not bounded is said to be unbounded. If f {\displaystyle f} is real-valued and f ( x ) ≤ A {\displaystyle f(x)\leq A} for all... from wikipedia.org