The base-2 progressive increase in dimensions seems to derive from shedding one axiom at a time. But isn't the number of axiom finite, indeed rather small? Doesn't this immediately imply that you get to zero axioms at a finite number of dimension. What is this maximum number of dimensions?

The alternative is that the number of axioms is infinite, but we start being unaware of this and are deluded into thinking we are making great progress when we shed a few of them.

And what makes real numbers the point of reference. Surely (giving up division) integers are a subset of reals, and (giving up subtraction) positive integers are a subset of those. Likewise modulus systems. Where does that end, with one or zero?