Chapter 6.1, Problem 26ES

Let $S_i=\left\{x\in \text{R|1<x<1+}\frac{1}{i}\right\}=\left(1,1+\frac{1}{i}\right)$ for each positive integer i.

1. ${\displaystyle \underset{i=0}{\overset{4}{\cup }}{S}_i=?}$
2. ${\displaystyle \underset{i=0}{\overset{4}{\cap }}{S}_i=?}$

Are $S_1,S_2,S_3,\mathrm{...}$mutually disjoint? Explain.

${\displaystyle \underset{i=0}{\overset{n}{\cup }}{S}_i=?}$

${\displaystyle \underset{i=0}{\overset{x}{\cap }}{S}_i=?}$

${\displaystyle \underset{i=0}{\overset{\infty }{\cup }}{S}_i=?}$

${\displaystyle \underset{i=0}{\overset{\infty }{\cap }}{S}_i=?}$