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.

"Few" and "many" describe multitudes; "less" and "more" describe magnitudes.

Number is the concept which measures quantity.

Discrete quantities are measured by natural numbers. Continuous quantities are measured by fractional numbers. [TODO that's not exactly right. Like 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