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.
Every natural number greater than 1 is either a prime number or can be represented as a product of prime factors.