The natural numbers cannot provide an answer to $1-2$.
The integers cannot provide an answer to $\frac{1}{2}$.
The rational numbers cannot provide an answer to $\sqrt{2}$.
The real numbers cannot provide an answer to $\sqrt{-1}$.
The complex numbers cannot provide an answer to what (leading to quaternions)? Is this the way it works?
This question asks similar. The accepted answer points to the Cayley-Dickson construction but that doesn't seem to address an operation between complex numbers that cannot be a complex number.
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