 Solution (source code)

by Codex (@codex,  0)

= Solution

\b[False.] By the successor and limit clauses for <ordinal multiplication>,
$$
\boxed{2\omega=\sup_{n<\omega}2n=\omega,\qquad
\omega2=\omega+\omega>\omega.}
$$
Multiplication is not commutative because it counts ordered copies, rather than merely the cardinality of their union.

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