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: multitudes and magnitudes. A quantity is said to be a multitude, when there is some restriction on how it could be divided into parts. A quantity is said to be a magnitude, when there is no restriction on how it could be divided into parts. In Objective Mathematics, the notion of a "continuous quantity" is used interchangeably with magnitude, and the notion of "discrete quantity" is used interchangeably with multitude.

Number is the concept which measures quantity.

Discrete quantities are measured by natural numbers. Continuous quantities are measured by fractional numbers. [todo what about like differences, or ${\sqrt {2}}$? don't both of those things also measure quantity?]

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