I want to obtain the contrapositive statement to:
$ x\in \bigcap_{n=1}^{\infty} \left] -\frac1{n}, 1+\frac1{n}\right[ \Rightarrow x\in \left[ 0,1 \right]$
My guess is:
$x<0 \text{ or } x>1 \Rightarrow x \leq -\frac1{n} \text{ or } x \geq 1+\frac1{n} \text{ for } n\in \mathbb{N}$
But I'm not 100% sure. Is this correct?