Solution
= Solution
The first assertion is \b[false]: $1<2$, but $1+\omega=2+\omega=\omega$. The second is \b[true]. In the concatenation definition of <ordinal addition>, the copy of $\alpha$ is a proper initial segment of the copy of $\beta$ when $\alpha<\beta$, so $\gamma+\alpha$ is a proper initial segment of $\gamma+\beta$.