Lambda edits

Advanced/Lambda Calculus/parts/03 numbers.tex

@@ -49,13 +49,9 @@ How about $(8~NOT~F)$?
 \pagebreak
 
 \problem{}
-This handout may remind you of Professor Oleg's handout on Peano's axioms. Good. \par
-Recall the tools we used to build the natural numbers: \par
-We had a zero element and a \say{successor} operation so that $1 \coloneqq S(0)$, $2 \coloneqq S(1)$, and so on.
-
-\vspace{1ex}
-
-Create a successor operation for the Church numerals. \par
+Peano's axioms state that we only need a zero element and a \say{successor} operation to
+build the natural numbers. We've already defined zero.
+Now, create a successor operation so that $1 \coloneqq S(0)$, $2 \coloneqq S(1)$, and so on. \par
 \hint{A good signature for this function is $\lm nfa$, or more clearly $\lm n.\lm fa$. Do you see why?}
 
 \begin{solution}
@@ -175,36 +171,5 @@ $D(1) = 0$, $D(2) = 1$, etc. $D(0)$ should be zero. \par
 	$D = \lm n . \Bigl[(~n~H~\langle 0, 0 \rangle~)~T\Bigr]$
 \end{solution}
 
-\begin{solution}
-	Here's a different solution. \par
-	Can you figure out how it works?
-
-	\vspace{1ex}
-
-	$
-	D_0 =
-	\lm p . \Bigl[p~T\Bigr]
-	\Bigl\langle
-		F ~,~ p~F
-	\Bigr\rangle
-	\Bigl\langle
-		F
-		~,~
-		\bigl\langle
-			p~F~T ~,~ ( (p~F~T)~(P~F~F) )
-		\bigr\rangle
-	\Bigr\rangle
-	$
-
-	\vspace{1ex}
-
-	$
-	D = \lm nfa .
-	\Bigl(
-		n D_0 \Bigl\langle T, \langle f, a \rangle \Bigr\rangle
-	\Bigr)~F~F
-	$
-\end{solution}
-
 \vfill
 \pagebreak