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I am having trouble picking a number x in the interval below. I need help picking the right interval. I tried sketching it, but I think I have trouble understanding it. Can someone help me clarify this? I have an exam coming up soon.

Thank You

enter image description here

user147271
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1 Answers1

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The irrational numbers are dense in $\mathbb {R}$ that means that for any $\delta> 0$ you will find an irrational number $ x$ in the interval $(a, a+\delta) $ or in $(a-\delta, a) $. It doesn't matter which irrational number is. The important thing is that such an irrational number does exist.

(Observe that in the solution, they don't care about which is the irrational $ x$ they pick, the only thing they care is the value of $ f (x) =2x$)

Joaquin Liniado
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