[cuspycode]

Yes, that was the most glaring mistake in the article, in my eyes. The runner up strange argument was the one about multiplication and addition having different identities and inverses. But why would the operations "Addition" and "Repeated Addition" have exactly the same properties? The operations are not the same.

I think the real issue is about how to interpret the adjective "Repeated" when we turn to more general domains than the natural numbers. But that's not a huge issue, it's mostly a matter of terminology.