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

Construct a sequence whose set of limit points is exactly the set of integers?

  • Thread starter hb1547
  • Start date
  • #1
35
0

Homework Statement


"Construct a sequence whose set of limit points is exactly the set of integers?"

The Attempt at a Solution


I need a sequence that will have an infinite number of terms that arrive at each of the integers, right?
And since the sequence is indexed by the natural numbers, doesn't that mean I need some kind of mapping from the natural numbers into the integers that meets that criteria?
 

Answers and Replies

  • #2
737
0
Yes, you need an (infinite) sequence that arrives at each of the integers (make this precise). I'd imagine you can think of several sets of numbers that satisfy this criteria. If these sets are countable, all that remains is to think of some way to map the naturals onto one of those sets. If you have a set in mind, we may be able to give you more targeted hints.
 
  • #3
35
0
My best guess was something like:

0, 0, -1, 1, 0, -1, 1, -2, 2, 0, -1, 1, -2, 2, -3, 3,....

Would that work?
 

Related Threads on Construct a sequence whose set of limit points is exactly the set of integers?

Replies
9
Views
2K
  • Last Post
Replies
11
Views
3K
  • Last Post
Replies
15
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
5
Views
1K
Replies
1
Views
1K
Replies
9
Views
1K
  • Last Post
Replies
7
Views
1K
Replies
11
Views
832
Replies
3
Views
284
Top