Is the system y[n] = x[n] + x[n-1] invertible?
Adjustment to https://math.stackexchange.com/questions/1453938/is-yn-xn-xn-1-invertible-system/1700642#1700642

Take 
$$ x_1[2n] = 1 \text{ and } x_1[2n-1] = -1 $$
and
$$ x_2[2n] = 2 \text{ and } x_2[2n-1] = -2 $$ for all \$n\in \mathbb{N}\$.  

Both have output \$y[n]=0 \$. The system cannot be inverted: one  output cannot distinguish at least two different inputs.