X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=exercises%2F_assignment4.mdwn;h=f998e7ac73a33c66d353463a62b91aa7b403d710;hp=fd9816dbfb3cc2a4eb0ffe8d9f0feb83312cc9d4;hb=ea4c96609b8d02f5e83a8027cf567bab5562cb5b;hpb=72b68b0bf93018ead47492255e87f1dd97827377

diff --git a/exercises/_assignment4.mdwn b/exercises/_assignment4.mdwn
index fd9816db..f998e7ac 100644
--- a/exercises/_assignment4.mdwn
+++ b/exercises/_assignment4.mdwn
@@ -96,8 +96,8 @@ addition, and exponentiation is defined in terms of multiplication.
 8.  Find a fixed point `ξ` for the successor function.  Prove it's a fixed
 point, i.e., demonstrate that `succ ξ <~~> ξ`.  
 
-    We've had surprising success embedding normal arithmetic in the lambda
-calculus, modeling the natural numbers, addition, multiplication, and
+    We've had surprising success embedding normal arithmetic in the Lambda
+Calculus, modeling the natural numbers, addition, multiplication, and
 so on.  But one thing that some versions of arithmetic supply is a
 notion of infinity, which we'll write as `inf`.  This object usually
 satisfies the following constraints, for any finite natural number `n`:
@@ -107,18 +107,18 @@ satisfies the following constraints, for any finite natural number `n`:
         n ^ inf == inf
         leq n inf == true
 
-    (Note, though, that with some notions of infinite numbers, operations like `+` and `*` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`.)
+    (Note, though, that with *some* notions of infinite numbers, like [[!wikipedia ordinal numbers]], operations like `+` and `*` are defined in such a way that `inf + n` is different from `n + inf`, and does exceed `inf`.)
 
-9. Prove that `add 1 ξ <~~> ξ`, where `ξ` is the fixed
-point you found in (1).  What about `add 2 ξ <~~> ξ`?  
+9. Prove that `add ξ 1 <~~> ξ`, where `ξ` is the fixed
+point you found in (1).  What about `add ξ 2 <~~> ξ`?  
 
 Comment: a fixed point for the successor function is an object such that it
 is unchanged after adding 1 to it.  It makes a certain amount of sense
 to use this object to model arithmetic infinity.  For instance,
 depending on implementation details, it might happen that `leq n ξ` is
 true for all (finite) natural numbers `n`.  However, the fixed point
-you found for `succ` may not be a fixed point for `mult n` or for
-`exp n`.
+you found for `succ` and `(+n)` (recall this is shorthand for `\x. add x n`) may not be a fixed point for `(*n)` or for
+`(^n)`.
 
 
 ## Mutually-recursive functions ##