Change N to Z+ in definition of congruence

content/sets-functions-relations/relations/equivalence-relations.tex

@@ -62,7 +62,7 @@
 
 \begin{ex}
 A nice example of equivalence relations comes from modular arithmetic.
-For any $a$, $b$, and $n \in \Nat$, say that $a \equiv_n b$ iff
+For any $a$, $b$, and $n \in \PosInt$, say that $a \equiv_n b$ iff
 dividing $a$ by~$n$ gives the same remainder as dividing $b$ by~$n$.
 (Somewhat more symbolically: $a \equiv_n b$ iff, for some $k \in
 \Int$, $a - b = kn$.) Now, $\equiv_n$ is an equivalence relation, for
@@ -77,7 +77,7 @@
 
 \begin{prob}
 Show that $\equiv_n$ is an equivalence relation, for any $n \in
-\Nat$, and that $\equivclass{\Nat}{\equiv_n}$ has exactly $n$ members.
+\PosInt$, and that $\equivclass{\Nat}{\equiv_n}$ has exactly $n$ members.
 \end{prob}
 
 \end{document}