Chapter 7.5, Problem 6E

(a)

To determine

To Find: The example of a sequence I of nested open interval such that ${\displaystyle \underset{n\in N}{\cap }{I}_n=\varphi }$ .

(b)

To determine

To Find: The example of a sequence I of nested open interval such that ${\displaystyle \underset{n\in N}{\cap }{I}_n}=\left(1,2\right]$ .

(c)

To determine

To Prove: The sequence I of nested close interval ${\displaystyle \underset{n\in N}{\cap }{I}_n}$ is non empty.

(d)

To determine

To Find: The example of a sequence I of nested open interval such that ${\displaystyle \underset{n\in N}{\cap }{I}_n}=\left[1,2\right]$ .

(e)

To determine

To Find: The example of a sequence I of nested open interval such that ${\displaystyle \underset{n\in N}{\cap }{I}_n}=\left\{1\right\}$ .