This preprint was written by a researcher at an accredited university with a PhD in physics. I'm sure they know what a vector valued function is.

The point of this paper is not to revolutionize how a scientific calculator functions overnight, its to establish a single binary operation that can reproduce the rest of the typical continuous elementary operations via repeated application, analogous to how a NAND or NOR gate creates all of the discrete logic gates. Hence, "continuous mathematics" as opposed to discrete mathematics. It seems to me you're being overly negative without solid reasoning.