- Whole Numbers
- |
- Properties of Whole Numbers
- |
- Closure Property
- |
- Commutative property
- |
- Associative property
- |
- Distributive property
- |
- Additive Identity
- |
- Multiplicative Identity
- |
- Multiplication by zero
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- Division by zero

We can say that whole nos. consist of zero and the natural numbers. Therefore, except zero all the whole nos. are natural 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.

The first 50 whole nos. are

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,14, 15, 16, 17, 18, 19, 20, 21,

22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,

41, 42, 43, 44, 45, 46, 47, 48, 49, 50

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. |

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. |

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

1)

a) 10702

b) 100500

c) 5100000

d) 5671

2)

a) 12

b) 99999

c) 8089

d)4320

0+2 =2

1+3=4

5+6=11

So Whole number are closed on Addition1+3=4

5+6=11

0X2 =0

1X4=4

5X1 =5

So Whole number are closed on Multiplication1X4=4

5X1 =5

5-0 = 5

0-5 =?

1-3 =?

3-1 =2

So Whole number are not closed on Subtraction0-5 =?

1-3 =?

3-1 =2

2/1= 2

1/2 =?

0/2= 0

2/0 =? ( Division by Zero is undefined)

So Whole Number are not closed on Division1/2 =?

0/2= 0

2/0 =? ( Division by Zero is undefined)

In short

Closure Property |
If a and b are any two whole numbers, then a+b, axb are also whole numbers. |

0+2 = 2+0=2

So Whole number are Commutative on Addition
0X2 =0 or 2X0=0

So Whole number are Commutative on Multiplication
5-0 = 5 but 0-5 =?

So Whole number are not Commutative on Subtraction
2/1= 2 but 1/2 =?

So Whole Number are not Commutative on DivisionIn 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×b = b×a. |

0+(2+3) = (0+2) +3=5

1+(2+3) =6= (1+2) +3

So Whole number are Associative on Addition1+(2+3) =6= (1+2) +3

0X(2X3) =0 or (0X2) X3=0

So Whole number are Associative on Multiplication
10-(2-1) = 9 but (10-2)-1 =7

So Whole number are not Associative on Subtraction
16 ÷ (4 ÷ 2) = 8 but (16 ÷4) ÷2 =2

So Whole Number are not Associative on DivisionSo in Short

If a, b and c are any two whole numbers, then (a+b)+c = a+(b+c) and (a×b)×c = a×(b×c).

2+0=2

0+3=3

5+0=5

1 × 1 =1

5 × 1=5

6 × 1=6

1 × 0 =0

5 × 0=0

0 × 0 =0

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