using notation for intervals [a,b] where a<=x<=b?

Question

the set goes from n=1 to 100,[1/n, 1 + 2/n] , The set is equal to an interval [a,b] give the values of a and b..the set is intersection as well..

the next part is to get it with the set being union,,its the same Q but how does that make the answer different?

intersection for the first part..union for the 2nd

the first part is taking the intersection from 1 to 100, [1/n, 1+2/n]

second part is the same question but with union

Answer 1

Write down the first few sets:
n=1: you have [1,3]
n=2: you have [1/2,2]
n=3: you have [1/3, 5/3]
n=4: you have [1/4, 3/2]
Now draw these on a number line. What happens as n->infty?

For the intersection, which numbers are in *all* of the sets? For example, the number 1 is in the first four sets. Can you show it is in all of them? Are there any other numbers that are in all of the sets? What does this say that the intersection is?

For the union, put all of the sets together and look at those numbers that are in at least one of your sets. Is anything more than 3 picked up? anything less that 0? How about 0 itself? how about those things between 0 and 3? What does this say that the union is?

Answer 2

Your question is not clear. Are you considering the sets individualy or are you taking the union or intersection?