diff --git a/Lectures/L17_MathReview/MathReview.pdf b/Lectures/L17_MathReview/MathReview.pdf index 4f21eac04abe70bcb4dee11cb29e49a3e455743a..7d80d91eef41551349bcccd8e94d4056f4d99fd8 100644 Binary files a/Lectures/L17_MathReview/MathReview.pdf and b/Lectures/L17_MathReview/MathReview.pdf differ diff --git a/Lectures/L17_MathReview/MathReview.tex b/Lectures/L17_MathReview/MathReview.tex index dc16d062b335ea151763ae15cc863a51cbf33eda..7d9ce6867fa21d860c28271f7e16a1481c3b3ef5 100755 --- a/Lectures/L17_MathReview/MathReview.tex +++ b/Lectures/L17_MathReview/MathReview.tex @@ -296,7 +296,7 @@ $*$ operators include $\forall$, $\exists$ and $+$ are used \begin{frame} %\frametitle{Quantifiers Example for Rank Function} -\noindent $\mbox{rank}(a, A): \mathbb{R} \times \mathbb{R}^n \rightarrow \mathbb{N}$\newline +\noindent $\mbox{rank}(a, A): \mathbb{R} \times \mathbb{R}^n \rightarrow \mathbb{R}$\newline $\mbox{rank}(a, A) \equiv \mbox{avg}(\mbox{indexSet}(a, \mbox{sort}(A)))$\newline \noindent $\mbox{indexSet}(a, B): \mathbb{R} \times \mathbb{R}^n \rightarrow \mbox{ set of } @@ -310,7 +310,7 @@ $\forall (a: \mathbb{R} | a \in A : \exists(b: \mathbb{R} | b \in B: b = a) \wedge \mbox{count}(a, A) = \mbox{count}(b, B)) \wedge \forall (i: \mathbb{N} | i \in [1..|A|-1] : B_i \leq B_{i+1})$\newline \noindent $\mbox{count}(a, A): \mathbb{R} \times \mathbb{R}^n \rightarrow \mathbb{N}$\newline -$\mbox{count}(a, A): + (x: \mathbb{N} | x \in A \wedge x = a : 1)$\newline +$\mbox{count}(a, A): + (x: \mathbb{R} | x \in A \wedge x = a : 1)$\newline \noindent $\mbox{avg}(C): \mbox{ set of } \mathbb{N} \rightarrow \mathbb{R}$\newline $\mbox{avg}(C) \equiv + (x: \mathbb{N} | x \in C : x) / |C|$\newline