Which of the following sets \(S\) have an upper bound and which have a lower bound? In the cases where these exist, state what the least upper bounds and greatest lower bounds are.

(i) \(S=\{-1,3,7,-2\}\).

(ii) \(S=\{x \mid x \in \mathbb{R}\) and \(|x-3|<|x+7|\}\).

(iii) \(S=\left\{x \mid x \in \mathbb{R}\right.\) and \(\left.x^{3}-3 x<0\right\}\).

(iv) \(S=\left\{x \mid x \in \mathbb{N}\right.\) and \(x^{2}=a^{2}+b^{2}\) for some \(\left.a, b \in \mathbb{N}\right\}\).