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elim 发表于 2024-6-6 04:23
\(\forall m\in\mathbb{N}\,(m\not\in A_m)\implies \forall m\in\mathbb{N}\,(m\not\in\displaystyle\bigc ...
根据定义\( A_n=\{k\in\mathbb{N}: k> n\}=\{n+1,n+2,\ldots\}\;(n\in\mathbb{N})\)有
\(\forall m∈\mathbb{N}\)\(\Longrightarrow (m+k)∈A_m\;\;\;(k∈\mathbb{N})\)\(\Longrightarrow (m+k)∈\displaystyle\bigcap_{n=1}^∞ A_n(m,k∈\mathbb{N})\)\(=\displaystyle\lim_{n→∞}\{n+1,n+2,n+3,…\}≠\phi\).〖因为趋向无穷的n由\(\displaystyle\bigcap_{n=1}^∞\)逻辑确定,所以(n→∞)时(n+1)随之确定。同理(n+2),(n+3)……也随确定,所以\(\displaystyle\lim_{n→∞}\{n+1,n+2,n+3,……\}≠\phi\).〗 |
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