Quick Bounds Question [ Sets]

Question

1) Let $S =\{(−1)^n\; \mid\; n \in \mathbb{Z}\}$ . What is the greatest lower bound of $S$?

-1 is the Lower bound. But is it also the greatest lower bound? Or does it not exist?

Thanks.

And also

2) Let $S = \{p^2\; \mid\; p \in \mathbb{N}\; \text{is prime}\}$, this is a countable set, right?

Answer 1

As for 1$st$ question - it might be helpful to write explicitly content of $S$ as for the second notice that $S \subseteq \mathbb{N},$ where $\mathbb{N}$ is a set of all natural numbers.