1. The difference (or subtraction) of two magnitudes is that magnitude which describes how
much the larger exceeds the smaller.
2. The difference of equal magnitudes is zero.
3. The sum (or addition) of two magnitudes is that magnitude whose difference with either of the
two magnitudes is either of the two magnitudes.
4. The quotient (or division) of two magnitudes is that magnitude that measures either magnitude
in terms of the other.
5. If a  unit  is divided by a magnitude into parts, then each of these parts of a unit, is called the
reciprocal of that magnitude.
6. Division by zero is undefined.
7. The product (or multiplication) of two magnitudes is the quotient of either magnitude
with the reciprocal of the other.
8. The difference of any magnitude and zero is the magnitude.

Observe that all the basic arithmetic operations are defined in terms of difference.

(*) It is only possible to measure magnitudes by comparing the same qualitatively or quantitatively, that is, the prior definition of difference is mandatory.