Question

Define integer's and its properties

Answer 1

$\star{\huge{\bf{\underline{\pink{Integers :}}}}}$

• Integers include natural numbers , zero and negatives of natural numbers.
• The absolute value of an integers is its numerical value regardless its sign.
• The sum of positive integers is equal to the sum of the absolute values of all integers and carries a positive sign.
• The sum of negative integers is equal to the sum of the absolute values of all the integers and carries a negative sign.
• The sum of one positive and one negative integers is equal to the difference of the absolute values of the two integers and carries the sign of the integers having large absolute value.
• when the sum of Two integers is zero then these two integers  are called additive inverse of each other .
• The product of a positive integer and a negative integer is a negative integer.
• The product of two negative integers or two positive integers is a positive integer.
• If even number of negative integers are multiplied  then the sign of the products is always  positive .
• If odd number of negative integers are multiplied then the sign of the products is always negative.

$\rule{200}2$

Answer 2

Question:

Define Integers and its properties .

Answer:

$\bold \red{ \underline{what \: is \: integers \: ?}}$

The collection of whole numbers and negative of the whole numbers together are called integers.

The collection 1, 2 , 3,..... are said to be positive integers and -1,-2,-3..... are said to be negative integers.

$\bold \red {\underline{properties \: of \: integers}}$

• '0' is neither negative nor positive integer.
• There is no smallest and greatest integer.
• Negative integers are smaller than positive integers.
• There are infinitely many or uncountable integers.
• All natural and whole numbers are integers.
• All integers are not natural and whole number.
• Multiplication of a positive and a negative integers is negative.
• Multiplication of two positive integers is positive.
• Multiplication of two negative integers is positive .
• Multiplication of odd number of negative integers is negative.
• Multiplication of even number of negative integers is positive.

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$\bold \green{additional \: information}$

$\bold{what \: is \: whole \: number \: ?}$

The natural numbers along with zero forms the collection of Whole numbers.

$\bold{what \: is \: natural \: number \: ?}$

All the counting numbers greater than 0 is called natural numbers.

The numbers from 1 onwards : 1,2,3, and so on is called natural numbers.