## A record of gremlin achievement

These are errors in the first printing. Most readers will have later printings of course, and these howlers will have been eliminated. If no person is credited with the glitch, I found it myself (each one an arrow to my heart). Errors of punctuation and of English are omitted, since the reader will be easily able to supply the correction her- or himself.
• Page 7. Proof of Proposition 1.1. Last line should read M(y-x) and not My -x. N.B. This error survives in the 2nd printing.
• Page 13. Exercise 1.2(h)(iii). The reversed capital E used there means there exists and is not defined until page 19 (thanks to Martyn Partridge, Intertype).
• Page 36. In 1.17(a) twiddles subscript R should just be twiddles. (thanks to Aaron Wilson, University of Bath).
• Page 37. Definition 1.12 (b). Both the inequalities in this definition should be non-strict (thanks to Verity Jeffery, Meridian School).
• Page 45. Proposition 2.4 should explicitly include the hypothesis that the binary operation is associative (thanks to Chuck Miller of the University of Melbourne, Australia).
• Page 46. Line 3 of the proof of Lemma 2.1: the multiplication dot should be raised above the line of the bottom of the letters. (thanks to Nicolai Vorobjov, University of Bath). N.B. This error survives in the 2nd printing.
• Page 52. Proof (sketch). Replace the pompous but inaccurate though it would be a remarkable first-year undergraduate...' by since 2p (p) = p^2 + p^2'. (thanks to Ewart Shaw of the University of Warwick, England). Note that this idiocy survives into the 3rd printing!
• Page 63. The displayed equation should end 13/2 rather than 11/2. (thanks to Dave Johnson, University of the West Indies). N.B. This error survives in the 2nd printing.
• Page 69. This equation is missing something crucial. Append the symbols =0', (thanks to Charles Cruickshank). N.B. This error survives into the 3rd printing!
• Page 65. The field axioms; 0+a = a = a+0 and 1*a = a = a*1 (thanks to Dave Johnson and to Andriy Oliinyk of Toronto, Canada). N.B. This error survives in the 2nd printing.
• Page 76. Second paragraph. The angles of a triangle sum to pi, and not to 2pi. Ouch! (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 77. Last line. Insert sin(alpha - beta) instead of sin(alpha + beta). (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 79. First paragraph. Multiples is spelled incorrectly, and the references to multiples of pi should, of course, be references to odd integer multiples of pi/2.
• Page 81. Page 81, line 7: should be log(x)=... (thanks to Carrie Rutherford, Queen Mary and Westfield College, London).
• Page 82. Line 2 Replace log(nx) by log(x^n).(Andriy Oliinyk) Note that this howler survives into the 3rd printing!
• Page 82. Definition 3.11. The quantity e is not a natural number (thanks to Edward Fraenkel) of the University of Bath. Note that this howler survives into the 3rd printing!
• Page 85. Line 2. There is a surplus i in the first expression, which should read (e to the power i theta + e to the power minus i theta)/2''.
• Page 86. The obvious abbreviation than should read tanh (Verity Jeffery).
• Page 87. Line 9. robust formula for arcsin t should read robust formula for arcsinh t.
• Page 88. First line after the displayed equation. Replace inversion'' by integration''. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 89. Last line of third paragraph. Integral multiple of 2pi should read integral multiple of 2pi/n. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 91. 5th paragraph. x=y=e^(2*pi*i/3) so xy=e^(4*pi*i/3)=e^(-2*pi*i/3). (Andriy Oliinyk). N.B. This error survives in the 2nd and 3rd printings.
• Page 92. Line 16. Chapter 7 should read Chapter 6. N.B. This error survives in the 2nd printing.
• Page 99. Equation 4.5 should read ||lambda x || = |lambda| dot ||x||. N.B. This error survives in the 2nd printing.
• Page 100. Last line of proof. |u|| should be ||u||. N.B. This error survives in the 2nd printing.
• Page 101. Question 4.1 should read (4.5) to (4.10)'' since one cannot justify a definition! N.B. This error survives in the 2nd printing.
• Page 107. Line -5: A right bracket has gone walkies. (Aaron Wilson).
• Page 109: A bad one this! At the bottom, the equations should read aX + bY = r and cX + dY = s. (Aaron Wilson)
• Page 110: The previous glitch propagates over the page. In line 2 replace the column pair m,n by the column pair r,s. (Aaron Wilson)
• Page 112: 2 lines after the displayed equation, replace (x_1 - x_3) by (x_2 - x_3) as the third factor. (Aaron Wilson)
• Page 117. Line -2: should say X is also a right inverse of A. (Carrie Rutherford).
• Page 118. Bottom line. Replace 1 be I_n. (Aaron Wilson)
• Page 145. Line 1 should read partition of G''.
• Page 146. Proof of Proposition 5.7. It is better to replace m by n throughout the proof. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 147. Proof of Proposition 5.8:
• Line 1: m should be n.
• Line 6: h is a typical element of H; perhaps the best way to fix things is to amend line 5 to read Thus if h = c^j...
• Page 156. Section 6.2 (i) should read: If a < b and 0 Page 157. The two references to the Law 6.2 should be references to law (iv) at the start of Section 6.2. These occur in the proof of Proposition 6.1. (Aaron Wilson)
• Page 158. Section 6.3, third paragraph should read reciprocals of natural numbers''. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 166. In the proof of Proposition 6.6, the second displayed line, remove the brackets round a_n - l, but keep the modulus signs. (Aaron Wilson)
• Page 172. The proof of Proposition 6.4 is garbled.(Dave Johnson).
• Page 173. Proof of Theorem 6,2, line 1. Replace the symbol for natural numbers by a capital N. (Aaron Wilson)
• Page 174. Line 3. Replace We have'' by For n greater than or equal to M we have''.
• Page 174. Line 4. a_m should be l.
• Page 174. Exercise 6.8(b). The inequality sign should not be strict.
• Page 182. Definition 7.1 ends with a superfluous right bracket.
• Page 184. Example 7.3 line 4. The function under discussion is i, not h.
• Page 182. Definition 7.1 ends with a superfluous right bracket.
• Page 188 Line 14 (first line of the second paragraph of the proof), D_M should be \overline{T_M}. (thanks to Victoria Gould, University of York). N.B. This error survives in the 2nd printing.
• Page 192. Line 3 of the proof of Theorem 7.2. Remove the modulus signs surrounding f(x_{k+1}). (Aaron Wilson)
• Page 194. Penultimate line of the proof of Theorem 7.3. Replace lim z_i by lim f(z_i).
• Page 195. Remark 7.1. Replace z by b twice. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 197-198, Proposition 7.2 and the preamble. This is not an error, but a matter of mathematical hygiene. It would have been better to define f(0) to be the gcd of 0 and 1, and so f(0)=1. With this variation f would be (just when you thought that it was safe to get back into the water) continuous at all irrational points and discontinuous at all rational points (thanks to my colleague Geoffrey Burton of the University of Bath).
• Page 198. Third to 5th lines. We have only given A_{-}. Of course A_{+} is the complement of A_{-} in the rationals. Line 8 : the rational number t corresponds...'' please.
• Page 199 Second paragraph. Capital B becomes capital X half way through the paragraph. Replace B by X throughout. Also in the antepenultimate line of the paragraph, that union is over the sets A(i)_{-}.
• Page 199 Definition 8.2. The final symbol for the natural numbers on the last line should be just a capital N. (Dave Johnson) N.B. This error survives in the 2nd printing.
• Page 201. Last line of the second paragraph: the inequalities must be strict (otherwise what is said is nonsense).
• Page 202. Last paragraph: strike out non-negative''. Change minus to plus in the three occurrences of ...ad - bc (to ...ad+bc). Replace could be'' by `is'', and make the final inequality of the page strict. What was I thinking? (Answer: Not about mathematics for sure).
• Page 203. Penultimate line. The double vertical lines around x should be single vertical lines.
• Page 206. When it says Duplicate the word 26 times it should really say make 26 adjacent copies of the word. You can do this by applying f_1 5 times to get 32 copies of the orginal word, and then erasing 6 copies by repeated application of f_2.
• Page 207. Answer to question 1.23. Replace pi by 1 throughout (5 instances).(Aaron Wilson)
If you find an unrecorded glitch in the book, please send an email to G.C.Smith@bath.ac.uk and get yourself thanked here and in any reprinted edition.