I don't really know much about math but like, if you take the entire set of natural numbers and graph it as a vector it'd be like a line of indeterminate distance right. And if you do the same thing with the set of integers it would be like a bidirectional vector of indeterminate distance.
Couldn't you just re-graph that as a plane, and just include a single abstract unit length for the Y axis that represents either positive or negative of indeterminate value to represent the set of integers without having to use bidirectional vectors? Like, for any number that's positive it stays at 0, and for any number that's negative it goes to 1.
Which leads to the intuitive question, is it possible to have number sets that are "gradients" of positivity and negativity, instead of just black and white, positive or negative? How would that work?
Am I making any sense?
