Introduction to descriptive set theory:
A set is a well-defined collection of things
The things belonging to a set are called it's members or elements. These elements may be objects, persons, letters, numbers or any items at all.
Well-defined means that given a member, there must be no doubt in deciding whether it belongs to, or does not belong to the given set. Example:-
A set of apples weighting 200 g or over is a well-defined.
A collection of heavy apples is not well-defined and so it not a set.
All elements are separated by a comma.
The elements should be enclosed in braces (”{ }”).
Sets are usually represented by capital letters.
The order in which the members appear is not important.
If one or more elements are repeated, the set remains the same.
A set may consist of a single member like, B = {National bird of India} = {Peacock}. If 'A' is a set and 'a' is an elements of this set, then “a belongs to A”
This article is about descriptive set theory and the topics in that.
Descriptive Set Theory-representation of a Set (notation):
A set is determined by its members or elements. This determination is brought out in the following three ways.
Roster method :-
The method of listing the elements inside the braces is called Roster method. Example :- A set of alphabets of the English language represented by P is written as :
P = {A , B , C , D , E , F , ….}
Description method :-
The method of listing a set by a well-defined statement or description is called description method.
Example :- {Vowels in English alphabet}
Set builder form :-
The method of listing the elements inside the braces by stating the rule or property or formula is known as Set builder form. Example :- If A is a set of a natural numbers less than 80, then it can be represented as, A = {x : x is a natural number and is less than 80} or as
A = {=x : x E N, x<80 br="br">
Types of Sets in Descriptive Set Theory:
Finite set
The elements are limited. Example :-
Natural number less then 60.
A = {1,2,3,4,5,6,7,.....}
Days of a week
W = {Monday, ….. , Sunday}
In finite set
Unlimited numbers of elements Example :-
Set of odd numbers
N = {1 , 3 , 5 , 7....}
Set of even numbers
E = {2 , 4 , 6 , 8....}
Empty set
No elements is represented
Set of odd numbers between 5 and 6
A = { }
30th day of February
D = { }
A set is a well-defined collection of things
The things belonging to a set are called it's members or elements. These elements may be objects, persons, letters, numbers or any items at all.
Well-defined means that given a member, there must be no doubt in deciding whether it belongs to, or does not belong to the given set. Example:-
A set of apples weighting 200 g or over is a well-defined.
A collection of heavy apples is not well-defined and so it not a set.
All elements are separated by a comma.
The elements should be enclosed in braces (”{ }”).
Sets are usually represented by capital letters.
The order in which the members appear is not important.
If one or more elements are repeated, the set remains the same.
A set may consist of a single member like, B = {National bird of India} = {Peacock}. If 'A' is a set and 'a' is an elements of this set, then “a belongs to A”
This article is about descriptive set theory and the topics in that.
Descriptive Set Theory-representation of a Set (notation):
A set is determined by its members or elements. This determination is brought out in the following three ways.
Roster method :-
The method of listing the elements inside the braces is called Roster method. Example :- A set of alphabets of the English language represented by P is written as :
P = {A , B , C , D , E , F , ….}
Description method :-
The method of listing a set by a well-defined statement or description is called description method.
Example :- {Vowels in English alphabet}
Set builder form :-
The method of listing the elements inside the braces by stating the rule or property or formula is known as Set builder form. Example :- If A is a set of a natural numbers less than 80, then it can be represented as, A = {x : x is a natural number and is less than 80} or as
A = {=x : x E N, x<80 br="br">
Types of Sets in Descriptive Set Theory:
Finite set
The elements are limited. Example :-
Natural number less then 60.
A = {1,2,3,4,5,6,7,.....}
Days of a week
W = {Monday, ….. , Sunday}
In finite set
Unlimited numbers of elements Example :-
Set of odd numbers
N = {1 , 3 , 5 , 7....}
Set of even numbers
E = {2 , 4 , 6 , 8....}
Empty set
No elements is represented
Set of odd numbers between 5 and 6
A = { }
30th day of February
D = { }
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