Definition of set in Mathematics

Contents

1 Definition of set
- 1.1 Examples
2 Set of numbers
3 Set of Numbers (Venn Diagram 1.1)
4 Conclusion from Venn diagram 1.1
5 Exercise 1.1

Definition of set

Definition of set ? What is Sets?

Set is a well defined collection of objects.

Set theory was develop by German mathematician Georg Cantor (1845 – 1918).

Well defined collection of objects means definition of the collection of object must be absolute with respect to all frame of reference.

Or in other word for defining set, all object in a collection must have same property

“Collection of most beautiful actress in Bollywood” is not a set because definition of beauty of an object is not absolute with respect to all frame of reference. Thus, it is not a well-defined collection.

Collection of mathematics books in a school library is a set because it is well-defined

Examples

Collection of all states in the Indian union is a set
Collection of past prime minister of the Indian union is a set
The set of the solution of equation x² – 9x + 20 = 0 is = {4,5}
The set of Even natural numbers less than 7 is = {2,4,6}
Collection of all apple i-phone in mobile shop is a set

Set of numbers

N: The set of natural numbers {1, 2, 3, 4, 5, 6, 7………}
W: The set of whole Numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ……}
Z: The set of all integers (…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 …}
Z+: The set of positive integers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11….} = N: Set of natural numbers
Z-: The set of negative integers {…… -7, -6, -5, -4, -3, -2, -1}
R: The set of real numbers { -4, -3.53, 0, 1, 2, 3, 4.7, √5. 10/3, ….}
R+: The set of positive real numbers {……7,1, 2, 3, 4.7, √5. 10/3, √20, 420 ….} =
(0, ∞)
R-: The set of negative real numbers {…. -4, -3.53, -2, -1.5, -1, -.5…} = (-∞, 0)
R₀+: The set of non-negative real numbers {0, 0.7,1, 2, 3, 4.7, √5. 10/3, √20, 420, 664 ….} = [0, ∞)
R0-: The set of non-positive real numbers {…. -4, -3.53, -2, -1.5, -1, -0.5, 0} = (-∞, 0]
Q: The set of all rational numbers {… -9, -7, -1/2, -1/8, 1, 3/4, 4, 9/2…}
Q+: The set of all positive rational numbers {1, 3/4, 4, 9/2,10, 12, …}
The set of even numbers: {…-8, -6, -4, -2, 0, 2, 4, 6, 8 …}
The set of odd numbers: {…-7, -5, -3, -1, 1, 3, -5, -7 …}
The set of prime numbers: {2, 3, 5, 7, 11, 13, 17, 19…}

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Set of Numbers (Venn Diagram 1.1)

definition of set of numbers by venn diagram

Venn diagram 1.1

Conclusion from Venn diagram 1.1

Natural numbers are subset of whole numbers or all natural numbers are whole number but reverse is not true
Whole numbers are subset of integers or all whole numbers are integers but reverse is not true
Integers are subset of rational numbers or all integers are rational number but reverse is not true
Rational and irrational numbers are subset of real numbers or all rational numbers are real number but reverse is not true
Real numbers are subset of complex numbers or all real numbers are complex numbers but reverse is not true
Natural numbers, whole numbers, integers, rational numbers, irrational numbers real numbers are subset of complex numbers

Exercise 1.1

Set theory (Definition of set) Class 11 Mock Test 1.1 (Exercise 1.1)

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