The theory of Math starts with a blank context. Then the ability to add is introduced; and ones are delivered as raw materials.
Natural Numbers as Templates
The first meanings built are natural numbers. They become templates for defining new operations called first-order ops. Note: “+” = “*1“
More Operations and New Numbers
Definition via fill-in-the-blank method leads to more operations and numbers. Only L-order ops and R-order ops for n =1,2 and 3 have been analyzed in the math literature to date.
Special Numbers
Certain combinations lead to special numbers. Special numbers are used to define basis numbers.
This new theoretical foundation for mathematics explains numbers and numeric operations. In addition to providing a basis for reasoning about what is known, this new theory provides for the construction and definition of new numbers. This foundation secures long sought after stability for mathematics which in turn contributes to the integrity of scientific knowledge.