Handout edits

Advanced/Definable Sets/parts/2 quantifiers.tex

@@ -60,9 +60,15 @@ Which are true in $\mathbb{R}^+_0$? \par
 
 \problem{}
 Does the order of $\forall$ and $\exists$ in a formula matter? \par
-What's the difference between $\exists x ~ \forall y ~ (x < y)$ and $\forall y ~ \exists x ~ (x < y)$? \par
+What's the difference between $\exists x ~ \forall y ~ (x \leq y)$ and $\forall y ~ \exists x ~ (x \leq y)$? \par
 \hint{In $\mathbb{R}^+$, the first is false and the second is true. $\mathbb{R}^+$ does not contain zero.}
 
+\begin{solution}
+	If $\exists x$ is inside $\forall y$, $x$ depends on $y$. We can have a different value of $x$ for every $y$. \par
+	If $\exists x$ is outside, $x$ is fixed \textit{before} we check all $y$.
+\end{solution}
+
+
 \vfill
 
 \problem{}