# Arithmetic/Types of Numbers/Natural Number

## Natural Number[edit]

The natural numbers are the ordinary counting numbers 1, 2, 3, ...

They can be expressed mathematically:

- ℕ = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... }

Some mathematicians consider 0 to be a natural number. Although not used in arithmetic, this convention is common in logic and computer science. ℕ⁰, ℕ₀ and ℤ₀+ unambiguously denote the set of non-negative integers, while ℕ*, ℕ⁺, ℕ₁ and ℤ+ unambiguously denote the set of positive integers.

The greatest natural number does not exist: for every possible natural number n, there exists n+1 which is also a natural number.

All natural numbers also belong to complex numbers.

## Even Number[edit]

Even numbers are natural numbers that are divisible by 2.

- 2ℕ = { 0, 2, 4, 6, 8, 10, 12, 14, ... }

## Odd Number[edit]

Odd numbers are natural numbers that are not divisible by 2.

- 2ℕ + 1 = { 1, 3, 5, 7, 9, 11, 13, 15...}

## Prime Number[edit]

Prime numbers are natural numbers that are only divisible by 1 and by itself.

- P = { 2, 3, 5, 7, 11, 13, 17, 19,...}

## Composite Number[edit]

Composite numbers are natural numbers that are the product of some prime numbers. For example:

- 4 = 2 * 2
- 12 = 2 * 2 * 3
- 15 = 3 * 5

Every natural number, except prime numbers and 1, is composite.

### One[edit]

1 is neither a prime nor composite number, as the number is *only* divisible my itself.