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Let $p$ is a product of two non-zero ordinal numbers. Knowing $p$ we can restore each of these two ordinals, right?

How can we denote each of these two ordinals (supposing we know the value of $p$)? I suspect, these may be called "projections", right?

  • 9
    No. $2 \times 3 = 1 \times 6$.2012-03-18

1 Answers 1

9

No, you can’t always reconstruct $\alpha$ and $\beta$ from $\alpha\cdot\beta$. For example, $n\cdot\omega=\omega$ for every non-zero finite ordinal $n$.