sukilot

I think this paper is refuting Conway (and others') proof of the claim that a set can be divided into 3+ parts without relying on the Axiom of Choice. It does so by observing that the proof only applies to sets that have an ordering, which is to say that there is an algorithm for picking an element from the set, which am extra constraint beyond having only a test for determining whether a known object is an element is in the set. It then goes on to prove that it is not possible to evenly divide a set that lacks such a selection algorithm.

Or something like that.

Formal logic is taught in Mathematical Logic class (intermediate, optional) or Discrete math (intro/intermediate, often not taken)

Geometry class in high school sometimes teaches some of it.

Computer science Binary logic teaches some of (De Morgan's laws)

Outside of New Math of the 1970s, it is a glaring omission from the curriculum.

Even enriched classes like Art of Problem Solving that put heavy emphasis on proofs, do not teach formal logic.

Implemented addition via:

      cos(wx) sin (wy) + sin(wx) cos(wy)

But how did it compute that intermediate addition?

Looks nice, but would benefit from longer examples (10+ lines) to really get a feel for things.

I suggest you reread the OP and ask questions, because you seem to have overlooked some of the ideas explained therein, such as transfinite ordinals.