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Compactness and contradiction

Terence Tao · original page

Publisher
American Mathematical Society
First published
2013
ISBN
978-0-8218-9492-7
Publication year 2013.

This continues my series of books derived from my blog.

Errata

13 corrections · 3 awaiting a page number

  1. p. ?In Section 1.3, “Wittingstein” should be “Wittgenstein”.
  2. p. 82The first a in “dips below a on a” should be in math mode.
  3. p. 92In the third display, $\eta(1/N)$ should be $\frac{1}{2} \eta(1/N)$.
  4. p. 94“quarternionic” should be “quaternionic” (two occurrences).
  5. p. ?In the paragraph before (3.17), (3.13) should be (3.12).
  6. p. 110“considing” should be “considering”.
  7. p. ?After equation (3.24), $c_{\eta,s} N^s$ should be $c_{\eta,s} N^{s+1}$. Also, all occurrences of $c_{\eta,s}$ in this section should be $C_{\eta,s}$ for consistency.
  8. p. 131in Section 3.10.2, at the end of the treatment of the non-transverse case, “the exponent of $K'$ here is positive” should be “the exponent of $K'$ here is negative”.
  9. p. 140In Theorem 4.3.5, “there exists $s$” should be “there exists $R$“. In the definition of the shift $T$ and the set $V_i$, $x_n, x_{n-1}, x_0$ should be $c_n, c_{n-1}, c_0$ respectively.
  10. p. 143The à in Arzelà-Ascoli is missing.
  11. p. 220?: In Section 5.4.1, all occurrences of $T_M A$ should be $T_A M$.
  12. p. 240A, H should be in math mode in “determine how likely A would have occurred… under hypothesis H”. The second display should have $\geq$ rather than >=. Just before and in the last display, the P(A_i) should have P in bold face. “infinity” should be $\infty$.
  13. p. 242after display: “$bfP(B|A)$” should be “${\bf P}(B|A)$.

Pre-errata (corrected in the published version)

2 corrections

  1. p. 78In the first paragraph, “at least the” should be “at least one of the”. In the second paragraph, “generated by $S_k$” and “generated by $e_1,\ldots,e_{m-1}$” should be “generated by $S_k, e_m$” and “generated by $S_k$” respectively. In the third paragraph, after the first sentence, add “We may take $N$ to be a normal subgroup of $\hbox{ker}(\phi)$“. In the last paragraph, replace “cannot grow polynomially” by “cannot grow exponentially (as otherwise the number of subsums of $A^n e_i$ for $i=1,\ldots,d$ and $n=1,\ldots,N$ would grow exponentially in $N$, contradicting the polynomial growth hypothesis)”
  2. p. 79footnote 12: replace the first sentence by “Proof: the algebraic integers $\alpha^n$ for natural number $n$ have bounded degree and all Galois conjugates bounded, so the minimal polynomials have bounded integer coefficients and must thus repeat themselves after finitely many $n$.”

Contributors

Thanks to all those who have contributed corrections. Corrections received on or before 2026-07-09 were reported by the readers listed below over the years; individual per-erratum attributions for these legacy entries were not preserved in migration.

Last updated: July 9, 2026.