X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=examples.tex;h=e0ffcb97a11ce5a97a2e837e7c994fd19714e1ae;hp=fbbe8608e002736fef5d43c3e0b49da9e9a2179c;hb=987368c596bfe23dbcbaf5260a0d7011c9d3fc1e;hpb=7a60af0c2fa38f05aecd84b530d3c5b87eaf3de7

diff --git a/examples.tex b/examples.tex
index fbbe860..e0ffcb9 100644
--- a/examples.tex
+++ b/examples.tex
@@ -28,7 +28,8 @@
   \begin{section}{Arrow}
     The identity operator on $V$ is $\identity{V}$. The composition of
     $f$ and $g$ is $\compose{f}{g}$. The inverse of $f$ is
-    $\inverse{f}$.
+    $\inverse{f}$. If $f$ is a function and $A$ is a subset of its
+    domain, then the preimage under $f$ of $A$ is $\preimage{f}{A}$.
   \end{section}
 
   \begin{section}{Common}
@@ -107,23 +108,24 @@
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
     but what if $W = V^{\perp}$? Then we wish to indicate that fact by
     writing $\directsumperp{V}{W}$. That operator should survive a
-    display equation, too:
+    display equation, too, and the weight of the circle should match
+    that of the usual direct sum operator.
     %
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     %
     Its form should also survive in different font sizes...
     \Large
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     \Huge
     \begin{align*}
       Z = \directsumperp{V}{W}\\
-      \oplus\oplusperp\oplus\oplusperp
+      \oplus \oplusperp \oplus \oplusperp
     \end{align*}
     \normalsize
   \end{section}