How do you prove that this function is bijective?
$f\colon (0,1)\longrightarrow \mathbb{R}$
$f(x)=\tan (\pi(x-1/2))$
In fact I want to show that $(0,1)$ is equivalent to $\mathbb{R}$ by proving that $f$ is bijective. Using Derivative concept and the Intermediate value theorem, it's easy to prove that is bijective, but I'm not allowed to use them.
Tuesday, August 2, 2016
elementary set theory - How do you prove that this function is bijective?
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