> To even claim the existence of negative numbers is to use a subtraction operator somewhere before you add it.

this is silly: if you have complex numbers, and multiplication, you can get subtraction out of it, and complex numbers are in a sense more fundamental than natural numbers so you should always start with complex numbers

if you start with complex numbers, you can get to negative numbers by i*i

i*i 2*i*i 3*i*i 4*i*i . . .
and rational negative numbers by

\sum _k=1 ^\infty \sum _j ^ \infty =0 i*i j / k etc

1 - 1 = 1+ (-1) = 1 + i*i*1