In this post,we give a geometrical proof of the rearrangement inequality via dot product of two vectors. For vectors $\mathbf{OA}=(a_1,\cdots,a_n)$ and $\mathbf{OB}=(b_1,\cdots,b_n)$ in $\mathbf{R}^n$,the dot product of $\mathbf{OA}$ and $\mathbf{OB}$ is denoted by $\mathbf{OA}\cdot\mathbf{OB}$,w ...
In this post,I prove inclusion-exclusion principle inductively.This principle can be found at Exercise 33 in Terence Tao's post 245A, Notes 3: Integration on abstract measure spaces, and the convergence theorems. (Inclusion-exclusion principle) Let $ {(X, {mathcal B}, ...
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