Proving why $\Bbb Z_{4} \rightarrow \Bbb Z_{6} \text{ given by } f(\overline x) = [2x+1] $ is not a function.
The map $f:\mathbb{Z}_3 \to \mathbb{Z}_6$ given by $f(x + 3\mathbb{Z}) = x + 6\mathbb{Z}$ is not well-defined