NUMBER SETS
Definition Of Number Sets
All the numbers in the Number System are classified into different sets and those sets are called as Number Sets.
More About Number Sets
The set of real numbers is divided into natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
Video Examples: Number Sets
Examples of Number Sets
N= {1, 2, 3....} is the set of natural numbers.
(0, 1, 2, 3....} is the set of whole numbers.
I = {...-3, -2, -1, 0, 1, 2, 3...} is the set of integers.
The numbers 2/3,3/5, 10.3, 102.25, etc. are rational numbers but not integers.
etc. are irrational numbers.
Solved Example on Number Sets
Ques: Identify the number that is simultaneously a rational number, an integer, a whole number, and a natural number.
Choices:
A. 53
B. 0
C. 
D.
Correct Answer: A
Solution:
Step 1: 0 is a whole number and an integer. [Whole numbers are {0, 1, 2, ...}, Integers are the set of whole numbers and their opposites.]
Step 2: 
is a mixed number, which can be written in the form of rational number as 
[A rational number is the ratio of two integers in the form a/b, where b ≠ 0.]
Step 3: is a negative rational number.
Step 4: 53 is a natural number. [Natural numbers are {1, 2, 3, ...}.]
Step 5: 53 is an integer, a whole number and it can also be written in the form of rational number as 53/1.
Step 6: So, 53 is at once a rational number, an integer, a whole number, and a natural number.
Quick Summary
- Number sets classify different types of numbers.
- Common number sets include natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
- Real numbers encompass all rational and irrational numbers.
🍎 Teacher Insights
Use visual aids like Venn diagrams to illustrate the relationships between different number sets. Emphasize the importance of precise definitions.🎓 Prerequisites
- Basic arithmetic
- Understanding of integers
Check Your Knowledge
Q1: Which of the following is both a rational number and an integer?
Q2: Which number set does 0 belong to, but not the natural numbers?
Frequently Asked Questions
Q: Is 0 a natural number?
A: No, 0 is a whole number but not a natural number. Natural numbers start from 1.
Q: Are all fractions rational numbers?
A: Yes, as long as the numerator and denominator are integers and the denominator is not zero.