Definition of Integers - Positive & Negative Integers | jmathslearning

Integers

An integer is a number that can be written without a fractional component that. It can be positive, negative or zero.It is denoted by "ℤ".

ℤ = { ....... –3, –2, –1, 0, 1, 2, 3, 4, 5, ........ }

Type of Integers 

1. Positive     Integers

2. Negative       Integers

3. Non-negative Integers

1. Positive Integers

Whole numbers greater than zero are called Positive Integers. It is also called Natural Numbers and denoted by "ℤ⁺". 

ℤ^{+ = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ....... }}

2. Negative Integers

A negative integer is an integer to the left of zero on the number line. It is less than zero.It is denoted by "ℤ⁻".

ℤ⁻ = { ........... ,−7, −6, −5, −4, −3, −2, −1}

3. Non-Negative Integers

An integer that is either 0 or positive. It is also called Whole Numbers and denoted by "ℤ^≠ ". Some Authors use symbol " ℤ^*".

 ℤ^≠ = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ....... }

We can understand Integers from a Number Line.

A number on the left is less than a number on the right.

we can understand with help of some examples.

3 is less than 5

-2 is less than 0

-5 is less than -2

A number on the right is greater than a number on the left.

we can understand with help of some examples.

11 is greater than 8.

0 is greater than -6.

-6 is greater than -11.

We can understand Integers from a Picture Diagram.