Proofs Book Errata
Major Errors
- Page 31, Exercise 1.4: I should have explicitly said that you are allowed to rotate the shapes.
- Page 32, Exercise 1.9: The 5 numbers from {1,2,...,8} should sum to 9 and the 6 numbers from {1,2,...,10} should sum to 11.
- 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. Also, as of 2023, this is no longer an open problem! It has been solved!
- Page 54, in the footnote I called something an "equation" when it is an "expression"
- 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 132, Exercise 3.41(e), the first symmetric difference symbol should be an intersection symbol
- 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 245, Exercise 5.13: I should have said x < y.
- Page 247, Exercise 5.22, line 2: "propositions" should be "statements"
- Page 249, 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 313, There is a technicality that I glossed over. To rigorously do it one needs to double the input in the Halting program. You can look up details online if you're interested.
- Page 315, in the first existence part, I needed to consider the case r=0 separately. In this case, just let q'=-q and r'=0 and it works.
- Page 363, Exercise 8.9, B should be the powerset of N, not just N.
- 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 fun to say.)
- Page 19, line 15: delete the word "an".
- Page 34, second line: "no three them" should be "no three of them"
- Page 35, Exercise 1.25: "now gimmicks" should be "no gimmicks"
- 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.
- Page 101, in the first paragraph after Definition 3.4, "is some sense" should be "in some sense"
- Page 127, Exercise 3.12: Switch out R for U, to match Theorem 3.16.
- 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 156, near the bottom, "fatorials" should be "factorials"
- Page 186, the first full bullet point on that page, line 3: "Your proofs should highlight" should be "Your pictures should highlight".
- Page 187, when combining fractions a + became a -. But once you get to the < line it still works out.
- Page 199, 2 lines above the bunnies: "an rediscovered" should be "and rediscovered".
- Page 208, right after Definition 5.1, "true of false" should be "true or false"
- Page 218, footnote 20, line 8: "held out has arm" should be "held out his arm".
- Page 227, right after the graph, "exists an c" should be "exists a c"
- Page 230, the second bullet point, line 1: delete the second "to be". Or the first one, your choice.
- Page 230, fourth bullet point, "sounds" should be "sound"
- Page 230, the second to last line before the footnotes: delete the duplicated "an".
- Page 231, sixth paragraph, "sometime called" should be "sometimes called"
- 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".
- Using the quadratic formula is entirely unnecessary, as its conclusion is immediate without using it.
- Page 276, footnote 19: "If do you" should be "If you do"
- Page 279, Exercise 6.13: "to the" should be "of the".
- Page 317, The line that starts "By some algebra..." starts correct, but ends with a q - q', rather than q'-q, and this typo is repeated a few more times during the rest of the proof. The proof is otherwise unaffected.
- Page 328, in Footnote 40, "them name" should be "then name"
- Page 344, the first diagram: The elements w, x, y and z should be in italics.
- Page 363, Exercise 8.7 (j), the codomain should be (-infinity,0].