Understanding the concept of number
created by @chasekwas
For more details:
https://www.academia.edu/89794682/Und...
One can't define abstract numbers without the monad (abstract UNIT, Book VII, Definition I) because natural numbers are MEASURES of special kinds of ratios, that is, ones where the antecedent (numerator) is a multiple of the abstract unit, and the abstract unit is the consequent (denominator). The whole idea of the Monad (abstract UNIT) is to do away with having to choose a unit magnitude every time. The abstract unit has no size or type. However, all the properties of geometric ratios and units are inherited by the abstract unit.