32. Let P, be the set of all polynomials of degree n with integer coefficients. Prove that P,, is countable. (Hint: A proof by induction is one method of approach.) 33 Use Exercise 22

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#32 please, and can you please use induction. Thanks

32. Let P, be the set of all polynomials of degree n with integer coefficients. Prove that P₁, is
countable. (Hint: A proof by induction is one method of approach.)
33. Use Exercise 32 to show that the set of all polynomials with integer coefficients is a countable
set.
34. Prove the following generalization of Theorem 0.17: If S is a countable set and (As) es is
SES
Transcribed Image Text:32. Let P, be the set of all polynomials of degree n with integer coefficients. Prove that P₁, is countable. (Hint: A proof by induction is one method of approach.) 33. Use Exercise 32 to show that the set of all polynomials with integer coefficients is a countable set. 34. Prove the following generalization of Theorem 0.17: If S is a countable set and (As) es is SES
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