Show that |R|=|(-1,1)|. Hint consider the function f: R-->(-1,1) defined by f(x)=x/|x|+1.
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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 $\displaystyle f(x)=f(y) \Rightarrow x=y$ 2) Show $\displaystyle \forall y \in (-1,1), \exists x \in \mathbb{R}:f(x)=y$
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