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Ordinal multiplication has always seemed backwards to me. $\alpha \times \beta$ is defined as the concatenation of $\beta$ copies of $\alpha$, not the other way 'round as one might expect.

Does this go back to Cantor? Or did someone else create this convention?

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  • $\begingroup$ I hesitate to edit the title myself, but it might be more precisely to the point to ask about the convention for ordinal mult, rather than just "definition"... which connotes something different. $\endgroup$ – paul garrett Jan 26 at 23:16
  • $\begingroup$ @paulgarrett Yes I can see that. But isn't the convention the definition? I'm not sure what the difference is. Unless you mean that the two possible conventions are essentially the same definition, as opposed to some completely different definition. I don't care if you want to edit it. A few weeks ago someone suggested adding some tags and I rejected the edit by mistake, if that person wants to try again I'll approve. $\endgroup$ – user4894 Jan 26 at 23:26
  • $\begingroup$ Yes, I did mean that the two different conventions really do "define" the same thing, it's just a notational thing, not mathematical. I'll edit your title, then, if you don't object. $\endgroup$ – paul garrett Jan 26 at 23:45
  • $\begingroup$ @paulgarrett You're right, it's the same definition. Different convention. You convinced me! $\endgroup$ – user4894 Jan 27 at 4:25
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Cantor at first defined multiplication of ordinals one way, then later (for what he thought were good reasons) switched to the opposite way. So YES it is due to Cantor.

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