real analysis - Is $f(n)=n$, where $nin mathbb Z$ with the Euclidean metric continuous on $mathbb Z$?

According to the definition of continuity, given any $n_0\in \mathbb Z$, $\forall \epsilon\gt0$, $\exists\delta>0$ such that $\forall n \in \mathbb Z$ and $d_X(n,n_0)\lt \delta \Rightarrow d_Y\bigl(f(n),f(n_0)\bigl)\lt \epsilon$ holds when $\delta=\epsilon$. So I conclude that this graphically discrete function is continuous... Is there anything wrong?