Supremum, infimum, max and min for $n(1+(-1)^{n})$

Question

My question is, if my assumption is correct, for the set $$A = \{ n(1+(-1)^{n}) : n \in \mathbb{N},n\geq 1\}$$ I think that when $n$ is odd we have $\sup A = 0, \inf A= 0, \max A = 0, \min A = 0 $, and for even $n$ we have $ \sup A= +\infty, \inf A= 4, \max A = does \, not \, exist, \min A = 4$.

Is this corrected or wrong? I thank you for your time already and have a nice day.

Answer 1

We have $A=\{a_1,a_2,a_3,...\},$ with

$$a_{2n}=4n$$

and

$$a_{2n-1}=0.$$

This gives

$$ \inf A= \min A =0,$$

$$ \sup A = \infty,$$

and $ \max A$ does not exist.