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diff --git a/week2.mdwn b/week2.mdwn
index 1e3aa2bc..bd86cbbf 100644
--- a/week2.mdwn
+++ b/week2.mdwn
@@ -318,6 +318,8 @@ will eta-reduce by n steps to:
 
 	\x. M
 
+When we add eta-reduction to our proof system, we end up reconstruing the meaning of `~~>` and `<~~>` and "normal form", all in terms that permit eta-reduction as well. Sometimes these expressions will be annotated to indicate whether only beta-reduction is allowed (<code>~~><sub>&beta;</sub></code>) or whether both beta- and eta-reduction is allowed (<code>~~><sub>&beta;&eta;</sub></code>).
+
 The logical system you get when eta-reduction is added to the proof system has the following property:
 
 >	if `M`, `N` are normal forms with no free variables, then <code>M &equiv; N</code> iff `M` and `N` behave the same with respect to every possible sequence of arguments.
@@ -328,7 +330,7 @@ That is, when `M` and `N` are (closed normal forms that are) syntactically disti
 N L<sub>1</sub> ... L<sub>n</sub> x y ~~> y
 </code></pre>
 
-That is, closed normal forms that are not just beta-reduced but also fully eta-reduced, will be syntactically different iff they yield different values for some arguments. That is, iff their extensions differ.
+That is, closed beta-plus-eta-normal forms will be syntactically different iff they yield different values for some arguments. That is, iff their extensions differ.
 
 So the proof theory with eta-reduction added is called "extensional," because its notion of normal form makes syntactic identity of closed normal forms coincide with extensional equivalence.