From 18cfe48ab7c7c543175fc7bb17e85a3ae7aca917 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Thu, 11 Sep 2014 11:40:46 -0400
Subject: Remove junk

---
 lecture/main.tex | 9 ---------
 1 file changed, 9 deletions(-)

diff --git a/lecture/main.tex b/lecture/main.tex
index bef50ba..8b273ca 100644
--- a/lecture/main.tex
+++ b/lecture/main.tex
@@ -305,15 +305,6 @@ that this expected number is constant.
     proof of the lemma.
 \end{proof}
 
-\begin{proof}
-    $\E(time to query(x)) \leq \E(number of full intervals containing x)\leq
-    \sum_{k=1}^\infty\sum_{intervals I, |I|=k, h(x)\in I} \Pr(full)$
-    $\sum_{k=1}^\infty k\max_I \Pr(I full)$
-    we need to show that the $\max$ is $O(1/k^3)$ so that the sum converges.
-    $(m=2n)$, $n=number of diff keys active$.
-    $$\Pr(I full) \leq \Pr\big(|L(I)-\E L(I)|\geq \E L(I)\big)$$
-\end{proof}
-
 \begin{proof}[Proof of Proposition~\ref{prop:unfinished}]
 By applying the previous lemma:
 \begin{align*}
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