逐步淘汰原则
定理7.1
设有N件事物，其中$$N_{\alpha}$$件有性质$$\alpha$$，$$N_{\beta}$$件有性质$$\beta,\cdots,N_{\alpha\beta}$$件兼有性质$$\alpha\mbox{及}\beta,\cdots,N_{\alpha\beta\gamma}$$件兼有性质$$\alpha,\beta\mbox{及}\gamma,\cdots$$，则此事物中之既无性质$$\alpha$$，又无性质$$\beta$$，又无性质$$\gamma,\cdots$$者之件数为
$$\begin{align}N-N_{\alpha}-N_{\beta}-\cdots\
+N_{\alpha\beta}+\cdots\
-N_{\alpha\beta\gamma}-\cdots\
+\cdots-\cdots\end{align}$$
定理7.2
若$$a,b,\cdots,k,l$$为任意非负之数，则
$$max(a,b,\cdots,k,l)=a+b+\cdots+k+l\
-min(a,b)\cdots-min(k,l)\
+min(a,b,c)+\cdots\
-\cdots+\cdots\
\pm min(a,b,\cdots,k,l)$$
定理7.3
$$[a_1,\cdots,a_n]=a_1\cdots a_n(a_1,a_2)^{-1}\cdots(a_{n-1},a_n)^{-1}(a_1,a_2,a_3)\cdots(a_1,\cdots,a_n)^{(-1)^{n+1}}$$
定理7.4
$$(a_1,a_2,\cdots,a_n)=a_1\cdots a_n[a_1,a_2]^{-1}\cdots[a_{n-1}a_n]^{-1}[a_1,a_2,a_3]\cdots[a_1,\cdots,a_n]^{(-1)^{n+1}}$$