WHAT ARE INTEGERS AND PROPERTIES ?

Integers

As we are now we'll known with natural numbers & for each natural number a (say), there is a number -a such that a+(-a) = 0. This, 1+(-1)= 0, 2+(-2)= 0, ......

The numbers ....,-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ... are called integers. 1, 2, 3, 4, ... are called position integers, while -1, -2, -3, -4, -5, ... are called negative integers. The integer 0(zero) is neither positive nore negative.

The set of integers is denoted by Z or I. It is clear that all the natural numbers and all the whole numbers are integers but all the integers are neither natural nor whole numbers.

Some properties of integers:

• Every integer is greater than every Negative integers
• Zero is greater than every negative integer and is less than every positive integer.
• Every negative integer is smaller than every positive integer.
• Given two positive integers, the one with the bigger absolute value is greater.
• Given two negative integers, the one with smaller absolute value is greater.

Absolute value: The absolute value of an integer is the whole number obtained by disregarding its sign.  The absolute value of an integer a is denoted by |a|

 Thus |-51| = (absolute value of -51) = 51,

          |0|= (absolute value of 0) = 0,a|.

          |-2| = (absolute value of -2) = 2,

          |43| = (absolute value of 43) =43.