diff --git a/content/sets-functions-relations/size-of-sets/reduction-alt.tex b/content/sets-functions-relations/size-of-sets/reduction-alt.tex
index b9f08ec2..09807d97 100644
--- a/content/sets-functions-relations/size-of-sets/reduction-alt.tex
+++ b/content/sets-functions-relations/size-of-sets/reduction-alt.tex
@@ -46,7 +46,7 @@
 \end{prob}
 
 \begin{proof}[Proof of {\olref[nen-alt]{thm:nonenum-pownat}} by reduction]
-For reductio, suppose that $\Pow{\Nat}$ is !!{enumerable}, and thus that
+For a reduction, suppose that $\Pow{\Nat}$ is !!{enumerable}, and thus that
 there is an enumeration of it, $N_{1}$, $N_{2}$, $N_{3}$, \dots
 
 Define the function $f \colon \Pow{\Nat} \to \Bin^\omega$ by letting
@@ -62,8 +62,8 @@
 
 It is also !!{surjective}: every string of $0$s and $1$s corresponds
 to some set of natural numbers, namely the one which has as its
-members those natural numbers  corresponding to the places where the string
-has~$1$s. More precisely, if $s \in \Bin^\omega$, then define $N
+members those natural numbers corresponding to the places where the string
+contains a~$1$s. More precisely, if $s \in \Bin^\omega$, then define $N
 \subseteq \Nat$ by:
 \[
 N = \Setabs{n \in \Nat}{s(n) = 1}