# Ordered Field Question

1. Feb 24, 2014

### teme92

1. The problem statement, all variables and given/known data

Prove that 139/159 is not an upper bound for the set of real numbers:

E ={(14n + 11)/(16n + 19): n ε N}
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2. Relevant equations

3. The attempt at a solution

Right so I let 14n + 11 = 139 and I got n=9.14. Since n is supposed to be natural and the answer I got for n isn't, can I deduce that 139/159 is not an upper bound for E?

2. Feb 24, 2014

### shortydeb

You have to find a positive integer such that if you plug it into (14n + 11)/(16n + 19) you get a number greater than 139/159.
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3. Feb 24, 2014

### teme92

Hey shortydeb thanks for the quick reply.

That is what I originally thought but do I not need to get a number n that lies before and after 139/159 but not exactly on it? Its very tedious work if that is the case :/

4. Feb 24, 2014

### shortydeb

Set (14n + 11)/(16n + 19) equal to 139/159 and see what you get for n.

5. Feb 24, 2014

### Ray Vickson

No. All you need do is find an integer n giving the fraction > 139/159. You do not need to find the "best" or "nearest" n, or anything like that.

6. Feb 24, 2014

### teme92

Ok I get it now so. Thanks for the help much appreciated