diff --git a/tutorials/online/sidenote-levels-of-understanding.html b/tutorials/online/sidenote-levels-of-understanding.html
index ee61567..7e86fc7 100644
--- a/tutorials/online/sidenote-levels-of-understanding.html
+++ b/tutorials/online/sidenote-levels-of-understanding.html
@@ -7,7 +7,7 @@
   <body>
     <h2>How to think about an Alloy model: 3 levels</h2>
 
-There are three basic levels of abstraction at which you can read an
+There are three basic levels of abstraction at which you can understand an
 Alloy model.
 <ul>
 <li> The highest level of abstraction is the OO paradigm.  This level
@@ -24,8 +24,8 @@ <h2>How to think about an Alloy model: 3 levels</h2>
 
 <hr WIDTH="50%">
 
-<p> Consider the following excerpt.  A signature <b><tt>sig
-    S</b></tt>, extending <b><tt>E</b></tt>, has a field
+<p> Consider the following excerpt.  A signature <b><tt>
+    S</b></tt>, extending signature <b><tt>E</b></tt>, has a field
     <b><tt>F</b></tt> of type <b><tt>T</b></tt>.
 
 <b><pre>
@@ -49,9 +49,25 @@ <h2>How to think about an Alloy model: 3 levels</h2>
       <b><tt>T</b></tt>
 <li> <b><tt>s</b></tt> is an instance of <b><tt>S</b></tt>
 <li> <b><tt>.</b></tt> accesses a field
+  so
 <li> <b><tt>s.F</b></tt> returns something of type <b><tt>T</b></tt>
 </ul>
-
+<hr WIDTH="50%">
+<p> The way to understand it in terms of set theory is as follows:
+    S is a set containing elements of a particular type
+    E is also a set containing elements of a particular type
+    F is a set that contains tuples of (S1->E1) where
+      S1 is an element from set S,
+      E1 is an element from set E,
+      -> is the relational operator
+
+    Think of the dot operator now in terms of sets;
+    S1.F would result in S1 being matched with every tuple in F and
+    the resulting set would contain only the elements of type T that
+    are related to S1.
+
+</p>
+    
 <hr WIDTH="50%">
 
 <p> The fragment can be safely read as being about sets, elements, and
