Question

1.What is the intersection of all the open intervals containing the closed interval [0,1]? Justify your answer.

2. What is the intersection of all the closed intervals containing the open interval (0,1)? Justify your answer.

Answer 1

Answer:

Step-by-step explanation:

1)

We can find an open interval $(-\frac{1}{n}, 1+\frac{1}{n})$. Which contains the closed interval $[0,1]$ when $n \to \infinity$

Therefore, the intersection of all the open intervals containing $[0,1[/tex[ is [tex][0,1]$

2)

We can find closed intervals containing $[0,1]$ in $(-\frac{1}{n}, 1+\frac{1}{n})$ when $n \to \infinity$

Since $(-\frac{1}{n}, 1+\frac{1}{n})$ is closed, the intersection of all those intervals containing $[0,1[/tex[ is  the closed interval [tex][0,1]$