deletions | additions       diff --git a/Monotonicity_TSP_For_all_p__.md b/Monotonicity_TSP_For_all_p__.md  index 1bb8b76..1591b99 100644  --- a/Monotonicity_TSP_For_all_p__.md  +++ b/Monotonicity_TSP_For_all_p__.md 
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For all \(p\in S', \not\in S\):  Let \(p_{i-1}, p_{i+1}\) be the points before and after \(p\) in our travelling-salesperson cycle. Let \(a,b\) be \(d(p_{i+1}, p), d(p_{i+1}, p)\). p)\) respectively.  By the triangle inequality \(c \leq a + b\). Therefore \(|TSP(S)| = L+a+b \leq L + c = |TSP(S_{/p})|\).  For all points