Is there a bijective map from $(0,1)$ to $\mathbb{R}$? I couldn't find a bijective map from $(0,1)$ to $\mathbb{R}$. Is there any example?
Here is a nice one ${}{}{}{}{}{}{}{}{}$, can you find the equation?
By virtue of http://natureofmathematics.wordpress.com/lecture-notes/cantor/, here's another picture. The interval at the bottom is $\mathbb{R}$.