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.

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