Accumulation points!

  • Thread starter nitro
  • Start date
  • #1
9
0

Homework Statement


is there are a set with countably infinite number of accumulation points?


Homework Equations



is there a set with exactly two distinct accumulation points?

The Attempt at a Solution


a set with two accumulation points might be: {1/n + (-1)^n}
i have no clue about the countably infinite one

hope someone could help!

thx a lot
 

Answers and Replies

  • #2
156
0

Homework Statement


is there are a set with countably infinite number of accumulation points?


Homework Equations



is there a set with exactly two distinct accumulation points?

The Attempt at a Solution


a set with two accumulation points might be: {1/n + (-1)^n}
i have no clue about the countably infinite one
Your idea is fine, but be sure to write it correctly (with an ": n in N").

I'd prefer not to spoon feed you an example for the other; rather, consider perhaps a set (in R) that depends on two natural numbers. Say, [tex]\{y_n, y_n + x_m: n, m \in \mathbb{N}\}[/tex], which you might construct so that [tex]\lim_{m\to\infty} x_m = 0[/tex] and so, for each fixed n, [tex]\lim_{m\to\infty} y_n+x_m=y_n.[/tex]
 
Last edited:
  • #3
9
0
aahaaaaaaa!! :)
thx a lot, i got it
 

Related Threads on Accumulation points!

  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
909
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
5
Views
850
  • Last Post
Replies
5
Views
522
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
Replies
4
Views
6K
  • Last Post
Replies
6
Views
3K
Top