deletions | additions       diff --git a/Intro.tex b/Intro.tex  index 6cdd28c..8fc26ae 100644  --- a/Intro.tex  +++ b/Intro.tex 
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\mathcal{J}(\Delta{t})-\mathcal{L}(\Delta{t})^2\geq 0  \end{equation}  \begin{equation}  \Delta{t}\int_{t_i}^{t_f}k(t)^{2}dt-\left[{\int_{t_i}^{t_f}k(t)dt\right]^{2}dt\geq0 \Delta{t}\int_{t_i}^{t_f}k(t)^{2}dt-\left[{\int_{t_i}}^{t_f}k(t)dt\right]^{2}dt\geq0  \end{equation}  Putting in the time dependent rate coefficient for a second order irreversible decay, the inequality becomes  \begin{equation}