(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that there is no strictly increasing function f: Q->R such that f(Q)=R. (Do not use a simple cardinality argument)

2. Relevant equations

The section involves montone functions, continuity and inverses. I believe the theorem to be used is that a monotone function on an interval has a continuous inverse, and the intermediate value theorem.

3. The attempt at a solution

In class, our professor said that f has a continuous inverse, but I'm not sure why exactly. From there, I realize you can use the intermediate value theorem to contradict the fact the inverse is continuous, by letting c belong to the irrationals and showing it is not in the image.

EDIT: I now have everything down to proving that a strictly increasing, onto function f:Q->R is continuous

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# Homework Help: Analysis: No strictly increasing fn such that f(Q)=R

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