The number $\omega - 1$ is greater than any integer $n \in \mathbb{Z}$.

The surreal number $\epsilon = \frac{1}{\omega}$ satisfies the property $\epsilon > 0$ and $\epsilon < \frac{1}{n}$ for all positive integers $n$.

The surreal number $\sqrt{\omega}$ is such that $(\sqrt{\omega})^2 = \omega$ and $\sqrt{\omega} > n$ for all $n \in \mathbb{Z}$.

The sum $\omega + (-\omega)$ is equal to $0$.