(a) The formulais not one to which the principle of recursive definition applies. Show tha...

(a) The formula

is not one to which the principle of recursive definition applies. Show that nevertheless there does exist a function  satisfying this formula. [Hint: Reformulate (*) so that the principle will apply and require h to be positive.]

(b) Show that the formula (*) of part (a) does not determine h uniquely. [Hint: If h is a positive function satisfying (*), let f(i) = h(i) for i ≠ 3, and let f(3) = −h(3).]

(c) Show that there is no function  satisfying the formula