**Resources for A Radical Approach to Real Analysis (2nd edition)**

Corrections

Corrections to the 2nd edition are listed below. For a list of those who have helped to identify these errors, click here.

page 14, Exercise 2.1.1, in part b, the vertices should be at (a, 1-a^2), (a + \delta, 1 - (a + \delta)^2), (a + 2\delta, 1 - (a + 2\delta)^2)

page 15: Exercise 2.1.2, last line, coordinates of first point should be (k 2^{-n}, 1-k^2 2^{-2n}).

page 16: Exercise 2.1.10.a, last line, "are all with" should read "are all within"

page 27: Exercise 2.3.11. This technique only works for x >= 4. For x = 2 or 3, find the square root of 1/2 = 1 – 1/2 or 3/4 = 1 – 1/4, respectively, then multiply your answer by 2.

page 28: Exercise 2.3.12. (1 + x)^2 should be (1 + x)^a.

page 54: The definition of $C^p$ and analytic functions ignores a very real distinction between $C^{\infty}$ functions and analytic functions. A function $f$ that is an analytic function at $x0$ must be $C^{\infty}$ on an open interval containing $x0$, but more than that, there must be an open interval containing $x0$ in which the power series at $x0$ converges to $f$. The example given on page 55 is precisely an example of a function that is $C^{\infty}$ for all $x$ but is{\it not\/} analytic at $x=0$.

page 56: Exercises 2.6.4 and 2.6.5. Delete the adjective analytic.

page 58: Figure 3.1, the label at the right endpoint of the interval should be $x$

page 59: line 2 should end with "... what do we mean by the"

Page 84: line 16, first term in the sequence should be 2/pi rather than 1/pi. .

page 103, Exercise 3.4.6.f. By "decimal fraction" I mean a number in decimal form

page 103, Exercise 3.4.12, "increasing" should be "strictly increasing"

page 106: equation (3.52) third term of the series exapnsion for F(x) should be f '(a)(x - a) rather than f(a) (x - a).

page 107: Theorem 3.11. The hypothesis should be that there is a neighborhood of x = a in which all derivatives of f exist rather than just that all deriviatives of f exist at x = a.

page 109: In "Definition: infinite limit and limit at infinity," line 4 should read

sufficiently close to $a$ (but not equal to $a$). That is to say, there is a $\delta > 0$ so that $0 < |x-a| < \delta$ implies that

page 112, exercise 3.5.3, second displayed inequality, condition should read "if $0 < \alpha < 1$"

page 113, Exercise 3.5.8, last expression in displayed equation should be $lim_{x \to 0} \frac{2x \sin(1/x) - \cos(1/x)}{1},$

page 122: first paragraph following Theorem 4.1: ... I want to emphasize what it [omit is] does

page 172: equation (5.5), in the limit after the equal sign, lim_{x \to 0} should be lim_{y \to 0}

page 202: Exercise 5.3.11. The reference should be to exercise 5.3.10, not 6.3.7.

page 212: Exercise 5.4.1.b., summand should be $\frac{n^2}{\sqrt{n!}}(x^n + x^{-n}), missing factorial in the denominator.

page 229: The proof of Lemma 6.3 contains an error. The fact that $x$ is the upper limit of the $x_n$ does not guarantee that $|x-x_n|$ can be made arbitarily small for sufficiently large $n$. To see a corrected proof, click here.

page 232: First displayed equation after (6.32) should be $|F(x+0) - f(x+2a)|$, missing closing parenthesis.

page 233: Definition of $g$ in first displayed equation, top line should be $|F(x+0) - F(x+2u)|, 0 < u \leq a,$

page 279: first display after (A.21): upper limit of integration should be k [not 1]