What ordinals correspond to tuples ordered lexicographically?

logic set-theory ordinals order-theory

Solution 1:

Remember that ordinal multiplication is NOT commutative.

You don't want $n_{k-1} \cdot \omega$ because that equals $\omega$.

You should write

$$\omega^{k-1} \cdot n_1+\cdots+ \omega \cdot n_{k-1} +n_k$$

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