Constant Continuity Adv. Calc 1

  • Thread starter chief12
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Homework Statement


suppose f: [a,b] ---> Q is continuous on [a,b]. prove that f is constant on [a,b].

Homework Equations





The Attempt at a Solution



Since there is at least one irrational number between every two rational numbers,
then for f to be continuous in the given scenario, f must be constant

stuck about showing it with delta/epsilon proof
 

Answers and Replies

  • #2
Dick
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I don't think you need any epsilons and deltas. Just use the intermediate value theorem.
 
  • #3
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I don't think you need any epsilons and deltas. Just use the intermediate value theorem.

can you explain more, a bit lost, test tomorrow
 
  • #4
Dick
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can you explain more, a bit lost, test tomorrow

Look up the intermediate value theorem and tell me what it says.
 

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