Solution for Exercise 02 from Chapter 02 in Baby Rudin

[ceciliachan1979]

This pull request provides the solution for Exercise 02, Chapter 02, from the third edition of Principles of Mathematical Analysis by Walter Rudin.

[ceciliachan1979]

Old PR note, rebased to main, found a minor typo, fixed, pending review.

[E7-87-83]

let F: TP \to \mathbb{A} be surjective mapping by mapping each tuple to i-th root of the corresponding polynomial.

Define r: TP \to \mathbb{N} be the injective mapping that map a tuple to the size of the tuple minus 2, i.e. (a_0, a_1, a_2, ..., a_n, i) are mapped to n.

Since F(TP) = \mathbb{A}, we can define b: \mathbb{A} \to \mathbb{N}, b(a) = min r(F^{-1}(a)).

b' is surjective by definition. But obviously not injective, for example, b(sqrt(2)) = b(sqrt(3)) = 2.

Following your idea/approach, you should prove a subset of TP to \mathbb{A} is bijective.