deletions | additions       diff --git a/sectionComparison_of.tex b/sectionComparison_of.tex  index b973e5b..a0f578e 100644  --- a/sectionComparison_of.tex  +++ b/sectionComparison_of.tex 
...
\textbf{\textit{Proposition 1.}} For all $b$, there exists  $$  a\left(b\right)\in\left(0,1\right)\mbox{,} a\left(b\right)\in\left(0,1\right),  $$  such that  $$  s^{*}\left(b,k\right)>\max\left(0,b-1/2\right)  \mbox{ if and only if }  k/b>a\left(b\right)\mbox{.} k/b>a\left(b\right).  $$  \bigskip{}