\(\Huge\color{red}{六证若\lim n\notin\mathbb{N},则\mathbb{N}=\phi}\)

春风晚霞

       由elim的【\(\forall k，m\in\mathbb{N}\)有\((m\ne\lim n-k=\)\(\lim n\)\(\notin\)\(\mathbb{N})\)】\(\iff\)\(k=n-m时,\)\(n-k=n-\)\((n-m)=m\)\(\iff\)\(\lim (n-k)=\)\(\lim m=m\)\(\notin\mathbb{N}\)\(\iff\)\(\forall m\notin\mathbb{N}\)\(\iff\mathbb{N}=\phi\)！