• Support PF! Buy your school textbooks, materials and every day products Here!

Indexed Collection of Sets ((

  • Thread starter rocomath
  • Start date
  • #1
1,752
1
Indexed Collection of Sets ... :(((

My notes are confusing me so bad, worst part is that we're not using our book till later on and that just kills me a lot. I'm very text-book because notes never make sense to me.

Let [tex]A_n=[0,n][/tex]

a) What numbers are in [tex]\bigcup_{n=1}^{\infty}A_n[/tex]?

b) What numbers are in [tex]\bigcap_{n=1}^{\infty}A_n[/tex]?

Ok, so I have an example here ...

If

[tex]I=\{1,2,3...\}[/tex]

[tex]A_i=[-i,i][/tex]

Then

[tex]\bigcup=\mathbb{R}[/tex]

[tex]\bigcap=[-1,1][/tex]

I honestly, can't remember how we got [-1,1]???

a) Since An goes from 0 to n, wouldn't that make [tex]\bigcup=[0,\infty)[/tex]???
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618


Sure. The union is [0,infinity). What's the intersection? In your example, the intersection is [-1,1] because the smallest index is 1. I'm not sure what's confusing you so seriously here? Draw a picture of the sets.
 
  • #3
1,752
1


Wouldn't my intersection for my example also be all real numbers? I could choose the smallest index within my set, which is 1. But I could continue choosing within the real number system, giving me an infinite amount of options.

[tex]\bigcap=\mathbb{R}[/tex]???
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618


Wouldn't my intersection for my example also be all real numbers? I could choose the smallest index within my set, which is 1. But I could continue choosing within the real number system, giving me an infinite amount of options.

[tex]\bigcap=\mathbb{R}[/tex]???
No, no, no. The smallest set in your system is A_1 All of the others include it. An element of the intersection has to be in ALL of the sets. The intersection is [0,1].
 
  • #5
1,752
1


OHHH!!! In ALL the sets, makes a lot of sense now.

Because once I move onto n=2, I would have 0, 1, 2, but going back to n=1, it doesn't contain 2.

YAYYY :) Thanks!!!
 

Related Threads for: Indexed Collection of Sets ((

  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
1K
Replies
4
Views
4K
  • Last Post
Replies
1
Views
941
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
1
Views
983
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
1K
Top