Acceleration-free Motion Models on Two-element Number Planes

„Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics.”
(Jordan Ellenberg, How not to be wrong)

I started to clarify the concepts of differential and integral calculus on two-element numbers, with the exception of complex numbers, of course, since its analysis is a well-developed area of mathematics. The article on the calculus was getting too long, so I will summarise its background, and more specifically the important connections between the two-element numbers – which form the basis for their analysis – in this paper. Some of the relations presented here have already been mentioned in my previous articles, but now I have listed the mathematical foundations in the context of differential and integral calculus, in preparation for it, adding new ones and their interpretation.

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