[Arithmetic 6] Set of natural numbers

I. SET $\mathbb{N}$ AND SET $\mathbb{N}^*$

_ The set of natural numbers is denoted by $\mathbb{N}$.

$\mathbb{N}$ = {0; 1; 2; 3; 4; 5; ...}

_ Every naturral number is represented by a point on the number ray. The point representing the natural number a on the number ray is called point a.

_ The set of non-zero natural number is denoted by $\mathbb{N}^*$.

$\mathbb{N}^*$ = {1; 2; 3; 4; 5; ...} or $\mathbb{N}^*$ = $\left\{ x\in\mathbb{N} / x \ne 0 \right\}$

II. THE ORDER IN THE NATURAL NUMBER SET

_ Of two point on a number ray (number ray is horizontal with the direction of the arrow going from left to right), left point represents the smaller number.

_ Write a $\le$ b to show that a < b or a = b. And write a $\ge$ b to show that a > b or a = b.

_ If a < b và b < c then a < c.

_ Two consecutive natural numbers have a difference by one unit.

_ Number 0 is the smallest natural number. There is no greatest natural number.

_ The set of natural numbers has an infinite number of elements.

III. WRITING NATURAL NUMBERS

_ A natural number can have one, two, three, etc digit(s).

Example:  Number 5 has one digit.

                Number 1005 has four digits.

_ In the decimal number system, ten units in one place make one unit in the preceding place.

Example: $555 = 5.100 + 5.10 + 5$

               $\overline {ab}  = a.10 + b$  (a $\ne$ 0)

               $\overline {abc}  = a.100 + b.10 + c$ (a $\ne$ 0)