Is there a Continuous Function f:R-->R Discontinuous at All Other Numbers?

Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
2 replies · 2K views
nikolany
Messages
4
Reaction score
0
Is there a function f:R-->R that is continuous at π and discontinuous at all other numbers?

Thx

 
Physics news on Phys.org

Discussion

Consider the function f(x)=0 for x irrational and f(x)=x for x rational. Where is that continuous? Can you modify that for your purposes?
 
Dick said:
Consider the function f(x)=0 for x irrational and f(x)=x for x rational. Where is that continuous? Can you modify that for your purposes?

So f(x)=(x-π)^18 for x rational and 0 otherwise should work I think!

Thank you very much
 

Similar threads

F:R->R, the fourth derivative of f is continuous for all x

  • sdff22
  • · Replies 3 ·
  • Calculus and Beyond Homework Help
Replies
3

Graduate Cardinality of continuous functions f:R->R.

  • MathematicalPhysicist
  • · Replies 14 ·
  • Set Theory, Logic, Probability, Statistics
Replies
14

Graduate Example of Function f:R-R where lim x→0 xf(1/x) ≠ 0

  • Trigger
  • · Replies 3 ·
  • Calculus
Replies
3

Graduate Paperback edn. Smolin and other numbers to watch

  • marcus
  • · Replies 2 ·
  • Beyond the Standard Models
Replies
2