Learning: http://theanalysisofdata.com/

MikTex+Texmaker: https://leavedcorn.pixnet.net/blog/post/24773932-%E6%96%B0%E6%89%8B%E5%AE%89%E8%A3%9Dlatex%E6%87%B6%E4%BA%BA%E6%95%99%E5%AD%B8(step-by-step)

Combinatorically Happy List: ($U$ is the universe $\Huge\textrm{:)}$)

• $\textrm{Exactly-IEP}_U(k)=\sum\limits_{j=k}^m(-1)^{j-k}\color{blue}{\binom{j}{k}}S_j.\quad$ // All I have for you is a word, TENET.
• $\textrm{Exactly-IEP(k)}=\sum\limits^{\large\color{blue}{\binom{m}{k}}}_{I\in S_k}\textrm{Exactly-IEP}_I(0).\quad$ // Superposition.
• $\textrm{At_Least-IEP}_U(k)=\sum\limits_{j=k}^m(-1)^{j-k}\color{blue}{\binom{j-1}{j-k}}S_j.\quad$ // Combinatorial proof dream.

People proving it by mechanical-memory idea: (They try to be an expert but machine somehow)

• $\textrm{Let }m>k: \sum\limits_{l=0}^{k}\sum\limits_{j=l}^m=\sum\limits_{j=0}^m\sum\limits_{l=0}^{\min(j,k)}$ // Independentness of addition.