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Question: 1. In this problem we will count polynomials.
(a) Consider polynomials of the form ax, where a ∈ N. How many such polynomials are there?
(b) Now consider polynomials of the form ax + b, where a,b ∈ N. How many such polynomials are there?
(c) Continue considering, and this time examine polynomials of the form ax2+bx+c, where a,b,c ∈ N. How many such polynomials are there?
(d) Finally, consider polynomials of the form anxn + an-1xn-1 + ··· + a1x+a0. How many such polynomials are there?
2. Challenge: Is the set of polynomials with integer coefficients countable or uncountable?
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