# What is the smallest natural number 1

The natural numbers = {0, 1, 2, 3, 4, ....} are the numbers of counting.

**Properties of natural numbers:**

- 0 is the smallest natural number.
- Every natural number has a unique one
**successor**. - There is no other natural number between a natural number n and its successor n + 1.
- There is no greatest natural number.
- The natural numbers are ordered.
- The representation on the number line results in isolated points.

**Basic arithmetic rules (axioms) for natural numbers:**

**Seclusion**

- If you add two natural numbers, you get a natural number again. The natural numbers are relative to the
**Addition completed**. - If you multiply two natural numbers, you get a natural number again. The natural numbers are relative to the
**Multiplication complete**. - With regard to subtraction and division, the natural numbers are not closed.

**Neutral element**

- 0 is the neutral element in terms of addition because n + 0 = n
- 1 is the neutral element in terms of multiplication because n * 1 = n

**Commutative law**

n + m = m + n | It is true Commutative law regarding the addition |

n * m = m * n | It is true Commutative law regarding the multiplication |

** Associative law**

(n + m) + p = n + (m + p) | It is true Associative law regarding the addition |

(n * m) * p = n * (m * p) | It is true Associative law regarding the multiplication |

** Distributive law**

(n + m) * p = n * p + m * p | It is true Distributive law. |

: i.e .: n, m, p are any natural numbers.

**Special natural numbers**

**Even numbers**are natural numbers that are divisible by 2.**Uneven numbers**are natural numbers that are not divisible by 2.- A
**Prime number**is a natural number that is greater than 1 and can only be divided by itself or 1.

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