Page 57: For the definition of a partition of A, we need nonempty subsets of A.

Page 59: For the proof of Proposition 6.18 (the division algorithm for polynomials), one either has to assume knowledge of rational numbers or that n(x) is monic.

Page 80: In the proof of Theorem 8.42, we invoke Proposition 8.32(ii) twice; it should be Proposition 8.32(iii).

Page 88: For Proposition 9.10(i) we need to assume that A is not empty.

Page 109: The proof of Theorem 11.8 can be simplified--there is no need to consider separate cases for x.

Page 125: For the definition of an algebraic number, we need a nonzero polynomial with integer coefficients.

"Logic moves in one direction, the direction of clarity, coherence and structure. Ambiguity moves in the other direction, that of fluidity, openness, and release. Mathematics moves back and forth between these two poles. [...] It is the interaction between these different aspects that gives mathematics its power."
William Byers (How Mathematicians Think, Princeton University Press, 2007)

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