Prove that the limit \begin{equation} \lim_{x\to\infty}\,x \end{equation} does not exist.

Problem: 

Prove that the limit
\begin{equation}
\lim_{x\to\infty}\,x
\end{equation}
does not exist.

Answer: 

The limit \begin{equation} \lim_{x\to\infty}\,x \end{equation} does not exist.