A function f : N -> N is said to be computable if there exists a program that takes x as input and produces f(x) as output.
(a) Prove or disprove: every increasing function f : N -> N (i.e. if x >= y, then f(x) >= f(y)) is computable.
(b) Prove or disprove: every decreasing function f : N -> N (i.e. if x >= y, then f(x) <= f(y)) is computable.