Union of Two Sets: Introductory Analysis Question

[ShengyaoLiang]

find:

a)

U [2 + 2/n , Pi - 1/n ]
n∈N.

"U" means union. "pi" means 3.1415926535...

b)

U [1 / （1+n） , 1/n ]
n∈N.

thank you so much

 

[Pseudo Statistic]

What's the problem you're having? It would help to take a look at the limits of each "interval" as n goes to infinity, and n=1. Since you're "unioning", you can get a rough idea on how it's going to look and whether one end of the interval becomes open or closed.

 

[HallsofIvy]

find:

a)

U [2 + 2/n , Pi - 1/n ]
n∈N.

"U" means union. "pi" means 3.1415926535...

Write down some of the intervals: when n= 1, [4, pi-1] is empty because pi-1< 4! when n= 2, [3,pi-1/2] is empty because pi- 1/2< 3! when n= 4, [4/3, pi- 1/3] is non-empty and is precisely that interval. It might be a good idea to draw a few of those on a number line. What is crucially important, as Pseudo Statistic said, is to see what 2+2/n and pi- 1/n converge to as n goes to infinity.

b)

U [1 / （1+n） , 1/n ]
n∈N.

thank you so much

When n= 1 this is [1/2,1], when n= 2, [1/3, 1/2], when n= 3, [1/4, 1/3]. Again, what happens to the endpoints as n goes to infinity? Remember that you are taking a union here.

 

[ShengyaoLiang]

thank you very much~~~