I am not sure how to do these quesions Thank u soooo much 1

I am not sure how to do these quesions. Thank u soooo much!

1. (a) Give an example of a countable collection of disjoint open intervals.

(b). Give an example of an uncountablee collection of disjoint open intervals, or argue that no such collection exists.

Solution

SOLUTION:

1.(a).    In set of all real number consider the collection of open intervals A={(n,n+1):n belongs to integer}.

That is A={ .......(-3,-2),(-2,-1),(-1,0),(0,1),(1,2),(2,3),(3,4),(4,5),......... so on}

This collection is a countable collection and no two intervals has coommon points.Hence a countable collection of disjoint open intervals.