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## Main Question or Discussion Point

I recently had a conversation with a friend (who for some reason likes number theory) about these split-complex numbers and dual numbers. I'm more into topology, so I've never heard of them and he brought up that the modulus (I've only heard this term used for complex numbers) of the split-complex numbers can be negative. I made the guess that the modulus was a norm. He said it wasn't and I asked him what exactly a modulus was and he said it was just some real-valued function.

So, in general what is the definition of a "modulus" that coincides its definitions on the reals, complex, dual, and split complex numbers?

So, in general what is the definition of a "modulus" that coincides its definitions on the reals, complex, dual, and split complex numbers?