# Arithmetic/Types of Numbers/Natural Number

## Natural Number

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, ... }

1 is the smallest natural number. 0 is NOT a natural number, it is a WHOLE NUMBER. Whole numbers are all natural numbers AND zero. That means, all positive numbers, NOT negative.

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

Even numbers are natural numbers that are divisible by 2.

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

## Odd Number

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

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

## Prime Number

Prime numbers are natural numbers that are only divisible by 1 and by itself. 1 is not considered prime.

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