Fix up css for the rahr and move changes to site

changes-draft.html

@@ -1,109 +1,3 @@
 This file is a draft of the new changes for http://www.jirka.org/ra/changes.html
 
-The theme of this revision is trying to fix all the minor issues and errata I
-could find, and improve clarity, but not make any large changes, nor add any
-content.  Perhaps the biggest change are 3 new exercises.  Two are there to
-fix an erratum, and one was sort of kind of hidden part of an old exercise.
-There are a few new explanatory sentences here and there,
-but nothing new beyond that.
-
-<li>Add a very short finite example of cartesian product after
-  Definition 0.3.10.
-<li>Make Definition 0.3.11 (function) a bit easier to read by explicitly
-  stating that it is the $y$ that is unique.
-<li>In Definition 0.3.11 (function), define codomain.  It does appear in at
-  least one place in the book, and it may be good for the sake of being a
-  reference book.
-<li>Example 0.3.32 is a bit too informal and just leaves out 0 and the
-  negatives, so add that.
-<li>Move the argument for why infimum and supremum are unique to right
-  after Definition 1.1.2 and note why this means that the notation is
-  well-defined.
-<li>In Definition 1.1.1 (ordered set), label "transitivity" and "trichotomy"
-<li>Remove the first sentence of the proof of Proposition 1.1.9 and just
-  give the example before the proof.  It is not really part of the "proof" of
-  the statement itself.
-<li>In the proof of Example 1.2.3, the second displayed estimate, the $h$ is
-  given as an equality, so the last $\leq$ is actually $=$.
-  Also show explicitly that $s-h &gt; 0$ to fix erratum.
-<li>Improve the wording of proof of 1.4.2, also in the same proof the sets
-  $A$ and $B$ were being defined but we only used $=$ and not $:=$.  Also,
-  change $b_k$ to just be any number in $(a_k,b_{k-1})$, that is simpler and
-  sufficient.
-<li>In Definition 2.1.9, move the "Some authors use the word monotonic." to a
-  footnote to simplify the definition.
-<li>After definition 2.1.9 mention $\{ n \}$ as an example of a monotone
-  increasing sequence.
-<li>Simplify the proof of Proposition 2.1.10.  Don't say anything about the
-  $B$, we never use the bound, just say the set of values is bounded, that is
-  good enough to compute the supremum.
-<li>After Definition 2.1.16, explicitly mention what we mean by a subsequence
-  by writing $x_{n_1},x_{n_2},x_{n_3},\ldots$.
-<li><b>Add Exercise 2.1.23</b>
-<li>In Proposition 2.2.11, recast the proof of unboundedness to not be a
-  contradiction proof.  It's the same idea, but it avoids having to explain
-  why it is a contradiction, and avoids a contradiction proof.
-<li>In Example 2.2.14, use $M$ instead of $N$ for consistency.
-<li><b>Add Exercise 2.3.20</b>
-<li>Before Proposition 2.5.6, make "tail of a series" a defined term and add
-  it to index.
-<li>Rephrase the last argument in the proof of Proposition 2.5.17 to be a
-  little bit more straightforward.
-<li><b>Add useful remark to Exercise 2.5.6.</b>
-<li><b>Add remark to Exercise 2.5.16 about starting the series, and that only
-  tails satisfy the hypotheses, so that students do not forget to check these
-  technicalities.</b>
-<li>Add footnote on $L=\infty$ to proof of Proposition 2.6.1
-<li>Add a better introductory sentence to cluster points in 3.1.1.
-<li>In Lemma 3.1.7 and Proposition 3.1.17, add $L \in {\mathbb{R}}$ to the
-  hypotheses, that makes it clearer that it is a given number.
-<li><b>Since every semester I get a question about Exercise 3.1.1, add a
-  parenthetical remark: Yes one must prove the limit is what one claims
-  it is.</b>
-<li><b>In Exercise 3.1.11, change "Then show $f(x) \to L$ as $x \to c$ for some
-  $L \in {\mathbb{R}}$" to "Then show that the limit of $f(x)$ as $x \to c$ exists."
-  Perhaps that will make students not start on the wrong path of starting with
-  some $L$ existing rather than proving that it exists.</b>
-<li>When proving the Thomae function (3.2.12) is continuous at irrational
-  numbers, note that since the limit of $\{ x_n \}$ is $c$, then every
-  rational number is in the sequence at most finitely many times.
-<li>At the end of example 3.2.13, mention that $g$ is in fact continuous on $B$.
-<li>After proof of Lemma 3.3.1, add a short paragraph highlighting the use of
-  Bolzano-Weierstrass, to emphasize the technique.  It changes the pagination
-  of 3.3 a tiny bit (inadvertently getting less jarring page breaks)
-<li>Reword slightly the end of the proof of Example 3.4.3 to improve clarity.
-<li>Add two lines of text after proof of Theorem 3.4.4 to make a similar
-  point as for 3.3.1, again changing pagination of the rest of 3.4 very
-  slightly.
-<li><b>The "In other words" of Exercise 4.1.14 is confusingly stated with an
-  inequality, while the way to prove it is simply with an equality, that was
-  a cut and paste typo.  Of course it is true with an inequality still.</b>
-<li><b>In Exercise 4.1.15 (simple L'Hospital's rule) note that the limit of the
-  quotient of derivatives must exist, no need to "suppose" it, we're assuming
-  here that the derivatives are continuous and the denominator is never
-  zero.  Also assume that $g(x)\not= 0$ if $x \not= c$.  While it can be
-  proved that $g(x) \not= 0$ in some neighborhood of $c$, that was not
-  intended in this simple version.</b>
-<li><b>Added Exercise 4.1.16 to keep this sort of exercise explicitly.  That
-  is, if $f'(c) > 0$, then show that $f(x)$ is negative a bit before $c$
-  and positive for a bit after $c$, thus zero only at $x=c$.</b>
-<li>Be a little bit more precise in the proof of Lemma 4.2.2 to say that
-  all the $x$ and the $y$ are still within $\delta$ of $c$.
-<li>In the proof of Proposition 4.2.6 (and also 4.2.7) note explicitly
-  that $[x,y] \subset I$ because $I$ is an interval.
-<li><b>In Exercise 4.2.9, add a note that the student needs to prove that
-  $g(x)$ is not zero for $x \not= c$ so that the left hand side of the
-  equality makes any sense at all.</b>
-<li><b>In Exercise 4.3.2, ask about the $d$th Taylor polynomial, not the
-  $(d+1)$th, that was a typo.  Though of course the exercise is still true
-  for $d+1$.</b>
-<li>In Definition 5.1.6 and proof of Proposition 5.1.7 use $\ell$ instead of
-  $m$ since $m$ is used all over the place for a minimum of the function.
-<li>In proof of 5.3.5, explicitly mention the domain of $F$ for clarity.
-<li>In Propositions 7.2.6 and 7.2.8 explicitly mention that the sets are
-  subsets of $X$.
-<li>Throughout get rid of the use of the word "any" where it could be ambiguous.
-<li>Fix a couple of uses of "=" where ":=" is more appropriate.
-<li>Improve the typesetting of some statements.
-<li>Some minor clarifications and tightening of the language a bit throughout
-  the book.
+<li>

changes2-draft.html

@@ -1,8 +1,3 @@
 This file is a draft of the new changes for http://www.jirka.org/ra/changes2.html
 
-<li>Make line in Figure 9.6 a bit bolder to make it easier to pick out.
-<li>In Proposition 10.3.7, use $\ell$ for the number of balls to make it
-  clear that the number is quite likely different from the number of
-  rectangles.
-<li>Fix a couple of uses of "=" where ":=" is more appropriate.
-<li>Some minor clarifications and fixes to style and grammar.
+<li>

extra.css

@@ -73,6 +73,6 @@ li { display: list-item; }
 }
 hr.rahr {
     border-style: none;
-    background-color: #666;
-    height: 1px;
+    height: 0px;
+    border-top: thin solid #666;
 }