Problem with $\sup A, \min A, \max A$ and $\inf A$.

Question

Having the set:
$A=\{\frac1n+(-1)^n:n\in \mathbb N\}$
I found with some process (separate it to $n=2k$ and $n=2k+1, k\in \mathbb N$) that $\sup A=\frac32,\inf A=-1 \notin A$, so $\min A$ doesn't exist. My problem is at $\max A$, because $n \in \mathbb N$, I thought that there isn't $\max A$, but in my book it's equal to $\frac32$.