Solution
= Solution
\b[False.] The <ordinal number>[ordinal] $\alpha=\omega\cdot2$ is a <limit ordinal>, but
$$
\boxed{\alpha\omega=(\omega\cdot2)\omega=\omega^2,
\qquad
\omega\alpha=\omega(\omega\cdot2)=\omega^2\cdot2.}
$$
= Solution
\b[False.] The <ordinal number>[ordinal] $\alpha=\omega\cdot2$ is a <limit ordinal>, but
$$
\boxed{\alpha\omega=(\omega\cdot2)\omega=\omega^2,
\qquad
\omega\alpha=\omega(\omega\cdot2)=\omega^2\cdot2.}
$$