Integers

Integers are whole numbers that include all negative, positive, and zero values. They can be represented on a number line with zero (0) in the middle, positive integers to the right, and negative integers to the left.

We can use a number line to locate the position of any integer. Here is a portion of a number line showing the positions of the integers:

Zero (0) is neutral and is neither positive nor negative.

Natural Numbers

Natural numbers are the set of positive integers and do not include zero:

1, 2, 3, 4, 5, \dots

Even and Odd Numbers

Even integers are numbers that are divisible by 2, including zero:

0, 2, 4, 6, 8, 10, 12, \dots

Odd integers are numbers that are not divisible by 2:

1, 3, 5, 7, 9, 11, \dots

Integers ending in 0, 2, 4, 6, and 8 are even, whereas numbers ending in 1, 3, 5, 7, and 9 are odd. Negative even integers are also considered even:

-2, -4, -6, -8, -10, \dots

Negative odd integers are considered odd:

-1, -3, -5, -7, -9, \dots

Properties of Even and Odd Numbers

The sum or difference of two even numbers is always even.

Similarly, the sum or difference of two odd numbers is also even.

However, the sum of an even number and an odd number is always odd.

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