Constant Continuity Adv. Calc 1

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Homework Help Overview

The problem involves proving that a continuous function from a closed interval [a,b] to the rational numbers Q is constant. This falls under the subject area of advanced calculus and continuity.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to argue that the continuity of the function implies it must be constant due to the presence of irrational numbers between rational numbers. Some participants suggest using the intermediate value theorem instead, questioning the necessity of a delta/epsilon proof.

Discussion Status

The discussion is exploring different approaches to the problem, with some participants providing guidance on using the intermediate value theorem. There is a sense of uncertainty, as the original poster expresses confusion and seeks further clarification.

Contextual Notes

The original poster mentions an impending test, indicating a time constraint that may affect their understanding and approach to the problem.

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
 
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I don't think you need any epsilons and deltas. Just use the intermediate value theorem.
 
Dick said:
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
 
chief12 said:
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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