Let An={x∈R:1n+1≤x≤n}A_n = \{x \in \mathbb{R} : \frac{1}{n+1} \le x \le n\}An={x∈R:n+11≤x≤n} for n∈Nn \in \mathbb{N}n∈N (natural numbers, starting from 1). Determine the set S=⋂n=1∞AnS = \bigcap_{n=1}^{\infty} A_nS=⋂n=1∞An.
(0,∞)(0, \infty)(0,∞)
[1/2,1][1/2, 1][1/2,1]
[0,1][0, 1][0,1]
[1/2,∞)[1/2, \infty)[1/2,∞)