Whole Numbers
As we know, we use
1, 2, 3, 4,... when we begin to count. They come naturally
when we start
counting. Hence, mathematicians call the counting numbers as
Natural numbers.
Predecessor
and successor
Given any natural
number, you can add 1 to that number and get the next number i.e. you get its
successor.
The successor of 16
is 16 + 1 = 17, that of 19 is 19 +1 = 20 and so on.
The number 16 comes
before 17, we say that the predecessor of 17 is 17–1=16,
the predecessor of
20 is 20 – 1 = 19, and so on.
Whole
Numbers
We have seen that
the number 1 has no predecessor in natural numbers. To the collection of
natural numbers we add zero as the predecessor for 1. The natural numbers along
with zero form the collection of whole numbers.
Properties
of Whole Numbers
1)
Sum of any two whole numbers is a whole number i.e. the collection
of whole numbers is closed under addition. This property is known as the closure property for
addition of whole numbers.
2)
The multiplication of two whole numbers is also found to be a
whole number again. We say that the system of whole numbers is closed under multiplication.
Closure property : Whole
numbers are closed under addition and also under multiplication.
1) The
whole numbers are not closed under subtraction.
2) The
whole numbers are not closed under division.
1) You can add two whole
numbers numbers
in any order. You will not get any pair of whole numbers for which the sum is
different when the order of addition is changed. This property is known as commutativity for
addition.
2) You
can multiply two whole numbers in any order. Thus, addition and
multiplication are commutative
for whole numbers.
3) Subtraction
is not commutative for whole numbers.
4) This
is associative property
for multiplication of whole numbers.
In Fig 2.1 (a), we have 2 × 3 dots in each box. So, the total number
of dots is (2 × 3) × 4 = 24.
In Fig 2.1 (b), each box has 3 × 4 dots, so in all there are 2 ×
(3 × 4) = 24 dots.
Thus, (2 × 3) × 4 = 2 × (3 × 4).
5) There
is no associative property for division.
There are numbers,
having exactly two factors 1 and the number itself. Such number are 2, 3, 5, 7,
11 etc. These numbers are prime
numbers.
There are numbers
having more than two factors like 4, 6, 8, 9, 10 and so on. These numbers are composite numbers.
2
is the smallest prime number which is even.
Every
prime number except 2 is odd.
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