Math Help - proof

1. proof

Show that |R|=|(-1,1)|. Hint consider the function f: R-->(-1,1) defined by f(x)=x/|x|+1.

2. Originally Posted by natewalker205
Show that |R|=|(-1,1)|. Hint consider the function f: R-->(-1,1) defined by f(x)=x/|x|+1.
You have to just show f is bijective.Where are you stuck?

1) Show $f(x)=f(y) \Rightarrow x=y$

2) Show $\forall y \in (-1,1), \exists x \in \mathbb{R}:f(x)=y$