Show that the set of polynomials with integer coefficients is countable. Such a polynomial is of the

form

a(n) x^n + a(n-1) x^(n-1) + ...+ a(1) x + a(0), where the a's are integers.

Show that n!^n tends to 0 as n tends to ?

If x is any fixed number, show that x^n! tends to 0 as n tends to ?.

21.

18. Show that the set of polynomials with integer coefficients is countable. Such a polynomial is of the form a(n) x^n + a(n-1) x^(n-1) + ...+ a(1) x + a(0), where the a's are integers. 19. Show that n!^n tends to 0 as n tends to co. 20. If x is any fixed number, show that x^n! tends to 0 as n tends to co