Ononot — For each positive integer n \ge 1, we define the set of real

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Set Theoryhard

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For each positive integer $n \ge 1$ , we define the set of real numbers: $T_n = \left\{ x \in \mathbb{R} : \cos(2^n \pi x) = 1 \right\}$ Determine the union $U = \bigcup_{n=1}^{\infty} T_n$ and the intersection $I = \bigcap_{n=1}^{\infty} T_n$ .