Quantity
[TODO under construction]
Quantity is an irreducible attribute of existents, and therefore it admits only an ostensive definition.
When one says that there is more or as much or less of A than there is of B, he is comparing the quantity of A to the quantity of B.
When one talks about adding to or subtracting from A, he is talking about a change in the quantity of A.
Quantity is the most fundamental concept of math. Other concepts almost as fundamental are shape and likelihood [TODO really? think about it].
We observe that quantity comes in two forms.
There are quantities which are discrete, where there is some restriction on which values it is possible for them to take.
There are quantities which are continuous, where there is no restriction on which values it is possible for them to take.
Number is the concept which measure quantity.
Discrete <-> multitude
Continuous <-> magnitude
Discrete quantities are measured by natural numbers. Continuous quantities are measured by fractional numbers.
Examples
Discrete quantities
The number of apples in the grocery store is a discrete quantity. Although...
The number of oxygen atoms in a room
The size, in bits, of some file on some computer
The number of ingredients in a recipe
The price of a washing machine
Continuous quantities
The height of a man
The speed of a car
The volume of a swimming pool
The weight of a bag of rice
The distance to the sun