Order Type Multiplication is Associative
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Theorem
Let $\alpha$, $\beta$ and $\gamma$ be order types of ordered sets.
Then:
- $\paren {\alpha \cdot \beta} \cdot \gamma = \alpha \cdot \paren {\beta \cdot \gamma}$
where $\cdot$ denotes order type multiplication.
Proof
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Sources
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations: Exercise $34 \ \text {(b)}$