1. A magnitude is the concept of size or dimension.
2. The comparison of any two magnitudes is called a ratio.
3. A ratio of two equal magnitudes is called a unit.
4. A magnitude that is completely measurable by another magnitude is a rational ratio of
magnitudes.
5. A rational ratio in which the antecedent and consequent magnitudes are related as
factor/multiple or multiple/factor, is called a number.
6. Any magnitude that is a multiple of a unit is called a natural number.
7. Zero is the idea of no magnitude.
8. A fraction is a ratio of two numbers.
9. If for any ratio, one magnitude is an exact multiple of the other, then such a ratio is a fraction if
and only if, each of the magnitudes are multiples of a unit.
10. If any magnitude or ratio of magnitudes cannot be completely measured, then it is called an
incommensurable magnitude or ratio of magnitudes.

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