Set edits

Advanced/Size of Sets/parts/0 sets.tex

@@ -22,11 +22,13 @@ Note that the \say{subset} symbol resembles the \say{less than or equal to} symb
 
 We can also write $\{a, b\} \subset \{a, b, c\}$, which denotes a \textit{strict subset.} \par
 The relationship between $\subseteq$ and $\subset$ is the same as the relationship between $\leq$ and $<$. \par
+In particular, if $A \subset B$, $A \subseteq B$ and $A \neq B$ \par
 For example, $\{a, b, c\} \subseteq \{a, b, c\}$ is true, but $\{a, b, c\} \subset \{a, b, c\}$ is false.
 
 
 \definition{}
 The \textit{empty set}, usually written $\varnothing$, is the unique set containing no elements. \par
+By definition, the empty set is a subset of every set. \par
 \note[Note]{The $\varnothing$ symbol is called \say{varnothing.} If you'd like to know why, ask an instructor.}
 
 \problem{}
@@ -70,6 +72,11 @@ What is the power set of $\{1, 2, 3\}$? \par
 Let $A$ be a set with $n$ elements. \par
 How many elements does $\mathcal{P}(A)$ have? \par
 \hint{Binary may help.}
+\vfill
+
+\problem{}
+Show that the set of all sets that do not contain themselves is not a set. \par
+
 
 \vfill
 \pagebreak