Question about adding numbers.

Take the operation (++) as the "successor" function from peano axioms: https://en.wikipedia.org/wiki/Peano_axioms

For example: 0++ = 1, (0++)++ = 2

Defining addition as follow:

0 + m := m.

(n++) + m := (n + m)++.

For example 3+2 = ((2++)+2) = (2+2)++ = ((1++)+2)++ = ((1+2)++)++ = (((0++)+2)++)++ = (((0+2)++)++)++ = ((2++)++)++ = 5

How to add two rational/real numbers with this definition? It's mind boggling because i just learned how to add and i can only do this way.