# Number

[https://en.wikipedia.org/wiki/Number](https://en.wikipedia.org/wiki/Number)

A **number** is a _mathematical primitive_, a concept that is not defined in terms of the previously defined concepts. Numbers, like all things in mathematics, lack physical form and only exist in the mind. Even there, a number lacks a more concrete manifestation, staying hidden underneath its symbolic representation. We rely on our intuition to understand the concept of a number apart from its numeric representation, but we use one of its representations (symbol, word, sign, gesture) to refer to it.

In terms of sets (set is also a mathematical primitive), a number is a property that sets with the same number of elements share. The number zero is represented by the empty set; the number three is represented by sets that contain exactly three elements. Under a different set theory, the number three is the set that contains all other sets that have three elements.

In terms of functions, in _Lambda Calculus_, numbers are represented through function application: the number of times a function is applied to its argument represents a certain number (so zero means a function is not applied at all, one means a function is applied once, two twice, and so on).

numerals are strings of digits used to indicate magnitude. They measure size - how big or small a quantity is.

the counting numbers are used to enumerate (count) the objects.

scalars are numbers that are used to measure size, or how big or small something is. They represent the magnitude of a quantity.
