mjo-set: adopt \powerset{} from mjo-common.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index cd615de16cbab3fc8381aac6aeb4039d945f5601..e11815ef7856b47f0dd5cb0e775c3272caeec427 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -132,8 +132,7 @@
       \unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
     \end{equation*}
     %
-    The powerset of $X$ displays nicely, as $\powerset{X}$. Finally,
-    we have the four standard types of intervals in $\Rn[1]$,
+    Finally, we have the four standard types of intervals in $\Rn[1]$,
     %
     \begin{align*}
       \intervaloo{a}{b} &= \setc{ x \in \Rn[1]}{ a < x < b },\\
@@ -192,7 +191,11 @@
     $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
     concept is the Moore-Penrose pseudoinverse of $L$, denoted by
     $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
-    $\rank{L}$.
+    $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+    real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+    respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+    simplify because the ``$n$'' does not indicate the arity of a
+    Cartesian product in this case.
 
     The span of a set $X$ is $\spanof{X}$, and its codimension is
     $\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The
@@ -258,11 +261,6 @@
     system to test them.
   \end{section}
 
-  \begin{section}{Miscellaneous}
-    The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
-    = 3$.
-  \end{section}
-
   \begin{section}{Proof by cases}
 
     \begin{proposition}
@@ -309,6 +307,11 @@
     \renewcommand{\baselinestretch}{1}
   \end{section}
 
+  \begin{section}{Set theory}
+    The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
+    = 3$, and its powerset is $\powerset{X}$.
+  \end{section}
+
   \begin{section}{Theorems}
     \begin{corollary}
       The