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User:Trovatore/Arithmetic and exponentiation in various numerical structures

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Many times, usually in the context of discussions about the expression , I have wanted to express certain ideas that I think are relevant, but it would be too long-winded inline, and also I didn't want to spend the time. So I'm hoping that pointers to this essay may prove useful.

Opening remarks

It is often claimed that the natural numbers form a subset of the integers, which in turn form a subset of the rational numbers, which in their turn form a subset of the real numbers.

For most purposes this is true.