deletions | additions       diff --git a/question_Linearity_Testing_Suppose_that__.tex b/question_Linearity_Testing_Suppose_that__.tex  index 14a2d6d..6ac2bba 100644  --- a/question_Linearity_Testing_Suppose_that__.tex  +++ b/question_Linearity_Testing_Suppose_that__.tex 
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$\Pr[f(z+r_1)+f(r_1)=f(z+r_2)+f(r_2)] \geq 1 - 2\epsilon$. (Hint:  suppose $f(r_1)+f(r_2) = f(r_1+r_2)$; what is the relationship  between $f(z+r_1)$ and $f(z+r_2)$?)  \item[(b)] Show that for every $z \in \{0,1\}^n$, there exists a  value $f'(z)$ such that $\Pr_r[f(z+r)+f(r)=f'(z)] \geq \frac{1}{2} +  \sqrt{\frac{1}{4}-\epsilon}$. (so the probability tends to 1 as  $\epsilon$ approaches zero) \end{itemize}