The numbers 1,2, 3, are called natural numbers or counting numbers.
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Let us add one more number i.e., zero (0), to the collection of natural numbers. Now the numbers are 0,1,2, … These numbers are called whole numbers
We can say that whole nos. consist of zero and the natural numbers. Therefore, except zero all the whole nos. are natural numbers.
Facts of Whole numbers
1) The smallest natural number is 1.
2) The number 0 is the first and the smallest whole nos.
3) There are infinitely many or uncountable number of whole-numbers.
4) All natural numbers are whole-numbers.
5) All whole-numbers are not natural numbers. For example, 0 is a whole-number but it is not a natural number.
41, 42, 43, 44, 45, 46, 47, 48, 49, 50 Some other Important terms to remember
SUCCESSOR
The successor of a whole number is the number obtained by adding 1 to it.
Clearly, the successor of 1 is 2; successor of 2 is 3; successor of 3 is 4 and so on.
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PREDECESSOR
The predecessor of a whole number is one less than the given number.
Clearly, the predecessor of 1 is 0; predecessor of 2 is 1; predecessor of 3 is 2 and so on.
The whole number 0 does not have any predecessor.
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Example
1) Write the successor of
(a) $10701$ (b) $100499$ (c) $5099999$ (d) $5670$
2) Write the predecessor of
(a) $14$ (b) $100000$ (c) $8090$ (d) $4321$ Solution
1)
a) $10702$
b) $100500$
c) $5100000$
d) $5671$
2)
a) $12$
b) $99999$
c) $8089$
d)$4320$
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Properties of Whole Numbers
Closure Property
Closure property on Addition for Whole Number
$0+2 =2$
$1+3=4$
$5+6=11$
So Whole number are closed on Addition Closure property on Multiplication for Whole Number
$0 \times 2 =0$
$1 \times 4=4$
$5 \times 1 =5$
So Whole number are closed on Multiplication Closure property on subtraction of Whole number
$5-0 = 5$
$0-5 =? $
$1-3 =? $
$3-1 =2$
So Whole number are not closed on Subtraction Closure property on Division of Whole number
$ \frac {2}{1}= 2$
$ \frac {1}{2} =?$
$ \frac {0}{2}= 0$
$ \frac {2}{0} =? $ ( Division by Zero is undefined)
So Whole Number are not closed on Division
In short
Closure Property
If a and b are any two whole numbers, then a+b, axb are also whole numbers.
Commutative property
Commutativity property on Addition for Whole Number
$0+2 = 2+0=2$
So Whole number are Commutative on Addition Commutativity property on Multiplication for Whole Number
$0 \times 2 =0 \; or \; 2 \times 0=0$
So Whole number are Commutative on Multiplication Commutativity property on subtraction of Whole number
$5-0 = 5$ but $0-5 =?$
So Whole number are not Commutative on Subtraction Commutativity property on Division of Whole number
$\frac {2}{1}= 2$Â Â but $\frac {1}{2} =?$
So Whole Number are not Commutative on Division
In short
You can add two whole numbers in any order. You can multiply two whole numbers in
any order.
Commutative property
If a and b are any two whole numbers, then $a+b = b+a$ and $a \times b = b \times a$
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Associative property
Associativity property on Addition for Whole Number
$0+(2+3) = (0+2) +3=5$
$1+(2+3) =6= (1+2) +3$
So Whole number are Associative on Addition Associativity property on Multiplication for Whole Number
