[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 $\mathbb{N}^*$.

$\mathbb{N}^*$ = $\left\{1; 2; 3; 4; 5; ...\right\}$ 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 $1\,005$ has four digits.

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

Example: $555 = 5 \cdot 100 + 5 \cdot 10 + 5$;

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

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