Let An={x∈R:sin(x)≥1−1n}A_n = \{x \in \mathbb{R} : \sin(x) \ge 1 - \frac{1}{n}\}An={x∈R:sin(x)≥1−n1} for each n∈Nn \in \mathbb{N}n∈N (starting from 1). Determine the set S=⋂n=1∞AnS = \bigcap_{n=1}^{\infty} A_nS=⋂n=1∞An.
∅\emptyset∅
{2kπ+π2:k∈Z}\{2k\pi + \frac{\pi}{2} : k \in \mathbb{Z}\}{2kπ+2π:k∈Z}
[−π2,π2][-\frac{\pi}{2}, \frac{\pi}{2}][−2π,2π]
{kπ:k∈Z}\{k\pi : k \in \mathbb{Z}\}{kπ:k∈Z}