Constant Continuity Adv. Calc 1

[chief12]

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

 

[Dick]

I don't think you need any epsilons and deltas. Just use the intermediate value theorem.

 

[chief12]

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

 

[Dick]

can you explain more, a bit lost, test tomorrow

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