Family Tree of Number
1. Natural
Numbers: Counting
numbers 1, 2, 3, 4, 5 … are called natural numbers.
2. Whole
Numbers: All counting
numbers together with zero form the set of whole numbers. 0,1,2,3,4,5
…
3. Integers: All
natural numbers, 0 and negatives of
counting numbers i.e.,…,−3,−2,−1,0,1,2,3,….. together form the set of integers.
(i) Positive
Integers: 1, 2, 3, 4….. is the set of all positive integers.
(ii)
Negative Integers: −1, −2, −3… is the set of all negative
integers.
(iii) Non-Positive
and Non-Negative Integers: 0 is neither positive nor negative.
4. Even
Numbers: A number
divisible by 2 is called an even number, ex. 2,4, 6, 8, etc.
5. Odd
Numbers: A number not
divisible by 2 is called an odd number. e.g. 1, 3, 5, 7,
9, 11 etc.
6. Prime
Numbers: A number
greater than 1 is called a prime number, if it has exactly two factors, namely
1 and the number itself.
7.
Composite Numbers: Numbers
greater than 1 which are not prime,
are known as composite numbers, e.g., 4,6,8,9,10,12.
8. Rational Numbers:
A rational number is a number that can
be in the form p/q , where p and q are integers and q is
not equal to zero. e.g : 1, 3, -1, 5/2, 3/7.
9. Irrational Numbers: An Irrational Number is a real number that cannot be written as a simple fraction. Irrational
means not Rational. e.g :
,
√2, √5, √8/11.
10. Real Numbers: All rational and irrational numbers are called. e.g : 3 , √8, √6/5, - √25, -5.
10. Real Numbers: All rational and irrational numbers are called. e.g : 3 , √8, √6/5, - √25, -5.
Notable Point:
1. 1 is neither prime nor composite.
2. 0 is neither positive nor negative.
3. 2 is the only even number which is prime.
4. There are 25 prime numbers between 1
and 100.
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