Positive Integers

Positive integers are numbers that are greater than 0. They include all whole numbers except 0, which is neither a positive nor a negative integer. The set of positive integers includes all counting numbers (natural numbers).

Examples

• 2, 4, 6, 8, 10
• 50, 51, 52, 53, 54
• 101, 102, 103, 104

Thus, when represented on a number line, they are the ones usually drawn on the right of zero.

Set of Positive Integers

It is a collection of positive integers that includes all whole numbers to the right of zero in the number line. In the roster form, the set is represented by the symbol Z, a superscript asterisk (*), and a subscript plus sign (+).

$\mathbb{Z}$*+ = {1, 2, 3, 4, 5,…}

The stylized Z was adopted from the German word for numbers ‘Zahlen’.

• It represents integers that can be positive, negative, and zero
• The asterisk signifies zero is excluded from the set of integers
• Plus sign means that negative numbers are excluded

The set consists of the first five positive integers that go on to infinity, as there is no end to counting positive integers. The ordering of $\mathbb{Z}$ is given by: {… −3 < −2 < −1 < 0 < 1 < 2 < 3 < …}

Thus, if we list the set of positive integers, it goes to infinity, where 1 is the smallest positive integer.

Operations with Positive Integers

Like natural numbers, addition, subtraction, multiplication, and division operations follow the same rule.

Addition

Adding 2 positive integers gives an integer with a positive sign

For example, (+3) + (+7) = +10

Subtraction

Subtraction between 2 positive integers is a normal subtraction and giving the sign of the greater number.

For example, (+5) – (+6) => 5 – 6 = -1

Multiplication

Multiplying a positive integer with a positive integer gives a positive integer.

Positive × Positive = Positive, for example, 8 × 4 => |8| × |4| = 32

Division

Dividing a positive integer with a positive integer gives a positive integer. Positive ÷ Positive = Positive, for example, (+36) ÷ (+6) => |36| ÷ |6| => 6