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How to prove if $m \in \mathbb{Z}$ and $n \in \mathbb{Z} \backslash \{ −1, 0 \}$ then $\frac{m + 1}{n+1} > \frac{m}{n}$ ?

I started by realizing $n \subset m$ and if we choose $x \in n$ it also means that $x \in m$. I don't know if I need to do that in order to prove the argument though and how to go on with it.

rtybase
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Joe
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  • n and m are not sets, to begin with – windircurse Oct 08 '17 at 09:07
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    The inequality fails for $m=2,;n = 1$. My guess is that you were asked to prove or disprove the claim. If so, one counterexample (such the one I just gave) suffices for a disproof. – quasi Oct 08 '17 at 09:08

1 Answers1

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For $m=n$ it's wrong.

$$\frac{m + 1}{n+1}-\frac{m}{n}=\frac{n-m}{n(n+1)}>0$$ for $n>m$.

Michael Rozenberg
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