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diff --git a/week1.mdwn b/week1.mdwn
index c9b52d1d..52654e3e 100644
--- a/week1.mdwn
+++ b/week1.mdwn
@@ -62,12 +62,19 @@ Some authors reserve the term "term" for just variables and abstracts. We'll pro
 Examples of expressions:
 
 	x
+	(y x)
+	(x x)
+	(\x y)
+	(\x x)
+	(\x (\y x))
+	(x (\x x))
+	((\x (x x)) (\x (x x)))
 
 The lambda calculus has an associated proof theory. For now, we can regard the
 proof theory as having just one rule, called the rule of **beta-reduction** or
 "beta-contraction". Suppose you have some expression of the form:
 
-	((\ a M) N)
+	((\a M) N)
 
 that is, an application of an abstract to some other expression. This compound form is called a **redex**, meaning it's a "beta-reducible expression." `(\a M)` is called the **head** of the redex; `N` is called the **argument**, and `M` is called the **body**.
 
@@ -278,18 +285,15 @@ It's possible to enhance the lambda calculus so that functions do get identified
 
 It's often said that dynamic systems are distinguished because they are the ones in which **order matters**. However, there are many ways in which order can matter. If we have a trivalent boolean system, for example---easily had in a purely functional calculus---we might choose to give a truth-table like this for "and":
 
-<pre><code>
-true and true   = true
-true and true   = true
-true and *      = *
-true and false  = false
-* and true      = *
-* and *         = *
-* and false     = *
-false and true  = false
-false and *     = false
-false and false = false
-</code></pre>
+	true and true   = true
+	true and *      = *
+	true and false  = false
+	* and true      = *
+	* and *         = *
+	* and false     = *
+	false and true  = false
+	false and *     = false
+	false and false = false
 
 And then we'd notice that `* and false` has a different intepretation than `false and *`. (The same phenomenon is already present with the material conditional in bivalent logics; but seeing that a non-symmetric semantics for `and` is available even for functional languages is instructive.)
 
@@ -534,7 +538,7 @@ Here's how it looks to say the same thing in various of these languages.
 
 		(let* [(bar (lambda (x) B))] M)
 
-	then wherever `bar` occurs in `M` (and isn't rebound by a more local "let" or "lambda"), it will be interpreted as the function `(lambda (x) B)`.
+	then wherever `bar` occurs in `M` (and isn't rebound by a more local `let` or `lambda`), it will be interpreted as the function `(lambda (x) B)`.
 
 	Similarly, in OCaml:
 
@@ -594,8 +598,7 @@ Here's how it looks to say the same thing in various of these languages.
 		let x = A;;
 		... rest of the file or interactive session ...
 
-	It's easy to be lulled into thinking this is a kind of imperative construction. *But it's not!* It's really just a shorthand for the compound "let"-expressions we've already been looking at, taking the maximum syntactically permissible scope. (Compare the "dot" convention in the lambda calculus, discussed above.)
-
+	It's easy to be lulled into thinking this is a kind of imperative construction. *But it's not!* It's really just a shorthand for the compound `let`-expressions we've already been looking at, taking the maximum syntactically permissible scope. (Compare the "dot" convention in the lambda calculus, discussed above.)
 
 9.	Some shorthand
 
@@ -667,9 +670,8 @@ Here's how it looks to say the same thing in various of these languages.
 
 	and there's no more mutation going on there than there is in:
 
-	<pre>
-	<code>&forall;x. (F x or &forall;x (not (F x)))</code>
-	</pre>
+	<pre><code>&forall;x. (F x or &forall;x (not (F x)))
+	</code></pre>
 
 	When a previously-bound variable is rebound in the way we see here, that's called **shadowing**: the outer binding is shadowed during the scope of the inner binding.
 
@@ -746,7 +748,7 @@ Or even:
 	(define foo B)
 	(foo 2)
 
-don't involve any changes or sequencing in the sense we're trying to identify. As we said, these programs are just syntactic variants of (single) compound syntactic structures involving "let"s and "lambda"s.
+don't involve any changes or sequencing in the sense we're trying to identify. As we said, these programs are just syntactic variants of (single) compound syntactic structures involving `let`s and `lambda`s.
 
 Since Scheme and OCaml also do permit imperatival constructions, they do have syntax for genuine sequencing. In Scheme it looks like this: