Find a formula that separate between structure

Question

I have language $ L = \{ < \} $.

I have the following structures:
$|M| = \{ 1-\frac{1}{m} |m\in Z, m >1\} $
$|N| = \{ 1-\frac{1}{m} - \frac{1}{n} |m,n\in Z, m,n >1\} $

I need to find a formula that separates the two structures

Any help with question will be appreciated. Thanks

Answer 1

As suggested by Martin Sleziak, not every element in $N$ has an immediate predecessor, while in $M$ every element has. For example, we have $\dfrac12 = 1 - \dfrac14 - \dfrac14$, which is approached by $1 - \dfrac12 - \dfrac1n$ for $n \to \infty$.

Thus, a sentence that is true in $M$ but not in $N$ is:

$$\forall x \exists y: y < x \land \forall z: z < x \to \neg (y < z)$$