Proofs Book Errata
Major Errors
- Page 31, Exercise 1.4: I should have explicitly said that you are allowed to rotate the shapes.
- Page 36, last paragraph of Exercise 1.26: We need to assume that n > 1.
- Page 39, I neglected to state a key detail about the Penrose tiling. The two shapes I showed have to be altered in some way to restrict how they fit together. See this for example.
- Page 84, Exercise 2.23: You should assume that a, b and c are integers.
- Page 115, the 4 lines of aligned equations beginning halfway down the page: Each ℝ in those sets should be a U.
- Page 189, Exercise 4.8: The product at the end of the exercise should start with F₀, not with F₁.
- Page 208, footnote 3, first line: "considered a sentence" should be "considered a statement"
- Page 214, footnote 14: "three propositions" should be "three statements"
- Page 221, Example 5.11, third bullet point: I claimed that was a false statement, but that is actually a true statement. I meant for the square root to be on the other n.
- Page 247, Exercise 5.22, line 2: "propositions" should be "statements"
- Page 5.27, Exercise 5.27: For all of the "There exists" statements, if that statement is false then there is no counterexample. So if you determine that one of those is false, just say so.
- Page 268, 6 lines above the Condensed, Elder-Approved Proof: I was joking around and wrote that skipping cases allows us to leave work early to spend more time with our kids. But I wrote "with kids" not "with our kids". Which sounds strange enough that I am labeling this a Major Error.
- Page 270, the final paragraph: (n+1)^16 + 9 should be (n+1)^19 + 6.
- Pages 298 and 299: The two propositions on those pages include "Prove that" at the start of their statements. Those two words should be deleted from each proposition.
- On page 304 I spoke with too much certainty about the Pythagorean story. Almost all details surrounding this story must be taken with a grain of salt. There remains no primary sources of this work, and there was so much mysticism built up around Pythagoras that it is hard to feel confident about the secondary sources.
- Page 309, the third bullet point: The 5 attached to the inner-most radical should be 6. Also, the second-inner-most radical should be multiplied by 5.
- Page 384, the forward direction of Theorem 9.5, as stated, is false. I should have been more careful with my wording. For the forward direction, the correct statement is that, given a partition of A, there is a (unique) equivalence relation whose equivalence classes are that partition. As stated, it allows for the counterexample A = {1,2}, and ~ being the relation a~b if a≠b. This ~ is not an equivalence relation, but for a 2-element set, it actually does create a partition.
Minor Errors
- Page 1, line 5: After "Why do we eat" is an extra apostrophe.
- Page 11, in the footnote: "fomula" should be "formula". (Although "fomula" is more to say.)
- Page 12, line 23: "Proofs also help us not just know math, but understand math" should be "Proofs also help us to not just know math, but to understand math".
- Page 19, line 15: delete the word "an".
- Page 31, Exercise 1.4: I should have explicitly said that you are also allowed to rotate the shapes.
- Page 34, second line: "no three them" should be "no three of them"
- Page 48, last line before the footnotes: at the word "by" before "showing".
- Page 66, last three lines: The final sentence should probably be deleted. It is not needed to prove part (iii).
- Page 83, Exercise 2.14, line 2: Delete the second time "down" was included.
- Pages 128 and 130: Exercises 3.19 and 3.31(b) are identical.
- Page 132, Exercise 3.43(b), second line: delete the duplicated use of the word "strip".
- Page 139, footnote: "vetices" should be "vertices".
- Page 186, the first full bullet point on that page, line 3: "Your proofs should highlight" should be "Your pictures should highlight".
- Page 199, 2 lines above the bunnies: "an rediscovered" should be "and rediscovered".
- Page 218, footnote 20, line 8: "held out has arm" should be "held out his arm".
- Page 230, the second bullet point, line 1: delete the second "to be". Or the first one, your choice.
- Page 230, the second to last line before the footnotes: delete the duplicated "an".
- Page 231, the 8th line from the bottom of the page: "speed or light" should be "speed of light".
- Page 243, Exercise 5.3(j): The number should be 8675309. This is the number from the famous song. Oh wait, not that one, it's from this song. And that number is indeed prime! I sang the song in my head when I typed it in with complete confidence that I wouldn't mess it up, and yet here we are...
- Page 264, the parenthetical right above Proposition 6.2: "I am feel" should be "I feel".
- Page 276, footnote 19: "If do you" should be "If you do"
- Page 344, the first diagram: The elements w, x, y and z should be in italics.