diff --git a/inputs/lecture_26.tex b/inputs/lecture_26.tex index 6909bad..dee889a 100644 --- a/inputs/lecture_26.tex +++ b/inputs/lecture_26.tex @@ -83,13 +83,10 @@ We do a second proof of \yaref{thm:hindman}: \footnote{Note that here we might need to choose a bigger $N$ than the $M$ in \yaref{def:unifrec}, but $2M$ suffices.}% - \[ - \forall n.~\exists N% \gg n - .~\forall r.~(y(r), y(r+1), \ldots, y(r+N - 1) - \text{ contains } - (y(0), y(1), \ldots, y(n)) - \text{ as a subsequence.} - \] + \begin{IEEEeqnarray*}{rl} + \forall n.~\exists N.~\forall r.~&(y(r), y(r+1), \ldots, y(r+N - 1)\\ + &\text{ contains } (y(0), y(1), \ldots, y(n)) \text{ as a subsequence.}\\ + \end{IEEEeqnarray*} \end{itemize} Consider $y(0)$.