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- Thread starter Amer
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- Thread starter
- #1

- Jan 26, 2012

- 890

Since between any two real numbers there is a rational, let \(p/q, \ p,q \in \mathbb{N}\) be such that:how to prove that for any real number in r (0,1) there exist a natural number n in N such that

rn > 1

\[\frac{r}{2}<\frac{p}{q}<r\]

Then multiplying through by \(q\) we get:

\[1\le {p}<rq\]

CB.

- Jan 30, 2012

- 2,525

I don't understand the question. What is "r (0,1)"? You want a numberhow to prove that for any real number in r (0,1) there exist a natural number n in N such that

rn > 1

- Jan 26, 2012

- 890

It should read:I don't understand the question. What is "r (0,1)"? You want a numbernsuch thatm> 1? If you want a number > 1, why not take 2?

What you have taken to be an "m" is in fact "r n" but with no space so that in the default font it looks like mProve that for any real number \(r \in (0,1)\) there exist a natural number \(n \in N\) such that \(r n > 1\)

CB

- Jan 30, 2012

- 2,525

Wow, talk about keming. It is true, I recently changed contact lenses and my vision went down a bit.What you have taken to be an "m" is in fact "r n" but with no space so that in the default font it looks like m