how do you prove that U( n=1) ( -1/n, 1/n) ={0}?

first i tried to prove that RHS ⊂ LHS..

then to prove that LHS ⊂ RHS, i tried to do it in cases..

assume that x>0, then 1/x>0... so for 1/x ∈ ( -1/n, 1/n) , it means that 1/x < 1/n..then how do i prove by contraction if that is the case?

or is my method wrong?