deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 90dd984..82a24b6 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\begin{proof}  \end{proof}  The above gives a characterization of the class of influence profile profiles  on which all opinion profiles converge. But we can also give a full characterization of convergence, i.e, we can also  characterize the class of opinion profiles which converge for graphs that do \emph{not} belong on this class: \begin{proposition}{}  Let $\G=(G_{p_1},\dots,G_{p_m})$ be an influence profile. Then the following are equivalent: 
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\end{itemize}  \end{proposition}  Below is yet  another way to put it: \begin{proposition}{}  Let $\G=(G_{p_1},\dots,G_{p_m})$ be an influence profile and $\O$ an opinion profile. Then the following are equivalent: