Give an example of a bijection from R to (0,1). A sketch graph that clearly indicates the key features of your example will suffice. Question: Give an example of a bijection from R to (0,1). A sketch graph that clearly indicates the key features of your example will suffice. Where I am at so far: I'm struggling with answering this question just by giving an example of a bijection. Is there an easy an easy bijection from R to (0,1)?

You can try the $\arctan$ function which takes $\mathbb{R}$ to $(-\pi/2, \pi/2)$ and shift it accordingly: $$\frac 1\pi \arctan(x) + \frac 12$$