$\lim\limits_{x\to0}\sin1/x$ What is
$$\lim\limits_{x\rightarrow0}{\left( \sin{\frac{1}{x}}\right)} $$?
Wolfram says "-1 to 1", but I don't know what that means. 
In fact, I thought this limit didn't exist, so what does "-1 to 1" mean in this context? 

The limit $$\lim_{x\rightarrow0}{\left( \sin{\frac{1}{x}}\right)}$$
does not exist. 
Note that as x approaches $0$, $\sin( 1/x )$ covers the closed interval  $[-1, 1]$ infinitely many times. 
For example at $ x= \frac {2}{(2n+1)\pi } $ we have $\sin(1/x)=\pm 1.$
Thus there is no limit for $\sin(1/x)$ as $x$ approaches $0$.
