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A Whole Number

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									                                    A Whole Number

A Whole Number
We have studied about the counting numbers. The numbers used for counting are called natural
numbers. 1, 2, 3, 4, ------- up to infinite are all natural numbers. If we add 0 to the set of natural
numbers, it becomes the set of whole numbers. This means, the set of whole numbers is 0, 1, 2 , 3,
………. up to infinite are called whole numbers. A set of whole numbers is used for various
measurements may it be distance, speed, weight , volume or any other measurement.

We observe that every natural number has a successor, which we can get by adding 1 to any given
whole number. For instance, successor of 245 is 245 + 1 = 246, successor of 890 is 890 + 1 = 891.
Similarly we see that every whole number except 0 has a predecessor, which we can get by subtracting
1 from the given number. As we can see, the predecessor of 45 is 45 – 1 = 44, predecessor of 900 is 900
– 1 = 899. Here are some of the properties of whole numbers :

1. Closure Property: If a, b are any whole numbers, then a+ b is also a whole number. We say that
whole numbers satisfy the closure property of addition,
2. Similarly according to the closure property of subtraction, if a , b are any two whole numbers such
that a > b, then a – b is also a whole number. E.g. if a = 9 and b = 4 , then a – b =9 – 4 = 5. Here we find
that a - b is also a whole number.

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    Math.Edurite.com                                                              Page : 1/3
3. Closure Property of multiplication also holds true, thus we can say that if a and b are whole numbers,
then a * b is also a whole number. E.g. if a = 3 and b = 5 then a * b = 3 * 5 = 15 is also a whole
number.

4. Closure property does not always holds true for the division operation, which means that if a, b are
whole numbers, then a / b is not necessary a whole number.

5. Commutative Property of whole numbers holds true of addition and multiplication but not for
subtraction and division : It says that if a and b are any two whole numbers then a + b = b + a and a *
b = b * a.

But we also have a – b ≠ b – a and a / b ≠ b /a

6. Additive Identity and Multiplicative Identity : If a is any whole number, then there exists a whole
number 0, such that a + 0 = a . Also there exists a whole number 1, such that a * 1 = a. So we can say
that 0 is the additive identity and 1 is the multiplicative identity. So we can say that if any number is
added to 0, the result is the original number, and if 1 is multiplied to any number, the result is the
original number.




                                          Read More About :- Properties of Rational Numbers


    Math.Edurite.com                                                           Page : 2/3
     Thank You




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