In Theorem 36 we saw that it is $\mathsf{NP}$-hard to $(1-\delta_0, 1)$-approximate Max-E$3$Sat for some positive but inexplicit constant $\delta_0$. You might wonder how large $\delta_0$ can be. The natural limit here is $\frac18$ because there is a very simple algorithm which satisfies a $\frac78$-fraction of the constraints in any Max-E$3$Sat instance:

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Ryan O'Donnell: Thanks!Ryan O'Donnell: Yeah, Chapter 13 doesn't exist. :( On the bright side, the ...Kirill Elagin: “In Chapter 13 we will show” =(Kirill Elagin: Typo (examples 22, bullet 2): “task is to fund”.Ryan O'Donnell: Argh! I specifically remember double-checking your name. G...Gautam Kamath: Thanks, I will wear this title with pride! As another (in...Ryan O'Donnell: Thanks Mom! For you, a free copy :)