I am sorry I should have written extensive and intensive properties.
That is quite different.
No I am not checking equations for correctness, I can't because I don't understand your rules of arithmetic.
Do you know how many axioms there are in Euclid?
So people often say that Euclidian Geometry is built on five axioms.
This is only a partial truth since those 5 axioms are supported by 23 definitions and a further 5 'common notions', effectively making 33 statements of axiomatic status in all.
I don't know what your equivalent support statements are so I would be in serious danger of mis-stepping.
Equally I can't see what you mean by your definition of infinity. (you have posted a great deal of text after all).
So please just quote it or something so it can be found.