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How to denote product of ordinals: $\cdot$ or $\times$?

I'm not sure which of these two multiplication symbols to use.

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    Don’t use $\times$. In my experience $\cdot$ is customary, though juxtaposition is also seen.2012-03-18

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The use of $ \times $ would be easily confused with the cartesian product, so it's not being used. I've seen both $ \alpha \cdot \beta $ and $ \alpha \beta $.