## Understanding Analysis

#### Stephen Abbott, Middlebury College

####
Springer,
New York, 2010

### Corrections (most of these have been corrected in the most recent printing)

page 24: Exercise 1.4.8d: insert "bounded" so it reads "A sequence of closed bounded (not necessarily nested) intervals..."

page. 55: Exercise 2.2.10 (c): Hypothesis should be " if (a_n) \rightarrow a"

page 71: Exercise 2.6.6b: add "or eventually monotone" to the end, so it reades "...that is not monotone or eventually monotone."

page 105: Exercise 3.4.3: "Theorem 3.4.2" should be "Example 3.4.2"

page 144: The corrected version of the 2nd edition removes the line saying that Young's result is "more intricate" and instead points out that a proof is possible. Specifically, combining the techniques in the two exercises mentioned (4.3.14, 4.6.2) with the Dirichlet-type defintions we have seen leads to such a proof.

page 162: Exercise 5.3.10: the function g(x) should be e^(-1/x^2). (Note the negative exponent.)

page 170: equation (2), 4x^4 should of course be 4x^3

page 171: line 13 should be 17th and 18th centuries (not 16th and 17th)

page 204: Exercise 6.6.4: The directions should be modified to read: "Explain how Lagrange's Remainder Theorem can be modified to prove..."

page 207: line 9, it should read "f(x)" not just "f".

page 223: Exercise 7.2.4: Delete "Is g necessarily continuous?"

page 236: Exercise 7.5.2(a): Replace "If h'=g" with "If g=h' for some h"