Merge branch 'master' of ssh://git.betalupi.com:33/Mark/ormc-handouts

Advanced/Definable Sets/parts/3 sets.tex

@@ -94,10 +94,10 @@ Consider the structure $S = ( \mathbb{R} ~|~ \{0, \diamond \} )$ \par
 The relation $a \diamond b$ holds if $| a - b | = 1$
 
 \problempart{}
-Define $\{\}$ in $S$.
+Define the empty set in $S$.
 
 \problempart{}
-Define ${-1, 1}$ in $S$.
+Define $\{-1, 1\}$ in $S$.
 
 \problempart{}
 Define $\{-2, 2\}$ in $S$.
@@ -116,7 +116,7 @@ Let $x \Bumpeq y$ be a relation on $P$. $x \Bumpeq y$ holds if $x \cap y \neq \{
 Show that $\Bumpeq$ is definable in $S$.
 
 \problempart{}
-Let $f$ be a function on $P$ defined by $f(x) = \mathbb{Z}^+_0 - x$. This is called the \textit{compliment} of the set $x$. \par
+Let $f$ be a function on $P$ defined by $f(x) = \mathbb{Z}^+_0 - x$. This is called the \textit{complement} of the set $x$. \par
 Show that $f$ is definable in $S$.
 
 \vfill