Solution
= Solution
\b[False.] Take $\alpha=\omega+1$, $\beta=2$. For finite $\gamma$, $\gamma\cdot2+\delta$ with $\delta<2$ is finite. For infinite $\gamma$, $\gamma\ge\omega$ implies $\gamma\cdot2\ge\omega\cdot2>\omega+1$. Neither case gives the required expression.