(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
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