Function Question

  • Thread starter neoking77
  • Start date
  • #1
31
0
Let f be the function that takes the value of 1 on all rational numbers, and 0 on all irrational numbers. At what points is f continuous?

Does anyone know how to do this?? I mean, there are just so many points to point out...such as square root of 2 and 10, and the list is endless...
 

Answers and Replies

  • #2
980
2
I'm fairly sure it's not continuous anywhere. Specifically, for any neighbourhood about any point, will contain some rationals and some irrationals, and so a sequence of decreasing neighbourhoods don't converge to any value.
 
  • #3
31
0
I see! Thanks a lot!
 

Related Threads on Function Question

  • Last Post
Replies
5
Views
827
  • Last Post
Replies
3
Views
10K
  • Last Post
Replies
13
Views
4K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
16
Views
2K
Top