$\lim\limits_{x\to0}\sin1/x$ 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? 

$$\Box \ \nexists \lim_{x\to 0}\bigg(\sin\frac1x\bigg).$$ Proof: Let $u = \dfrac{1}{x}$ then $$\lim_{x\to 0}\frac{1}{x} = \infty$$ since $$\lim_{x\to\infty}\frac{1}{x} = 0.$$ Therefore, we get $$\lim_{x\to 0}\bigg(\sin\frac 1x\bigg) = \lim_{u\to\infty}(\sin u)$$ but this cannot exist because sine is a periodic fluctuating function. $\qquad \qquad\qquad\qquad\quad\,\,\,\,$
