Can I prove "Let $\alpha,\beta$ and $\gamma$ be ornidal numbers. If $\alpha \cdot \beta = \alpha \cdot \gamma$ and $\alpha > 0$, then $\beta=\gamma$."?
2026-04-04 04:07:19.1775275639
Multiplication on ordinal number
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Let $0 < \alpha$ and $\beta < \gamma$. Then $$ \alpha \cdot \beta < (\alpha \cdot \beta) + \alpha = \alpha \cdot(\beta +1) \le \alpha \cdot \gamma. $$