A collection of well-defined and distinct objects is called a set in mathematics.
Well-defined collection means we can whether the object belongs collection or not and distinct means no two of which are the same.
We are familiar with the set since the word is frequently used in everyday speech for instance water set, tea set, sofa set. It is a wonder that mathematicians have developed this ordinary word into a mathematical concept. It becomes a language employed in more branches of modern mathematics.
The object in a set in mathematics is called members or elements.
Generally, we denote the set with capital letters A, B, C, D, etc., and elements with small letters a,b,c,d, etc.
How many ways to describe a set:
There are three ways to describe a set
- Descriptive method
- Tabular method
- Set builder notation
Descriptive method of set:
In this method, a set may be described in words. For instance,
e.g, D = A set of natural numbers.
Tabular Method of set:
A set may be described by listing its elements within brackets. If D is the set mentioned above, then we may write: D= {1,2, 3, 4…}
Set-builder notation:
It is sometimes more suitable. The method of set-builder notation in framing sets. This is done by using a symbol or letter for an unpredictable member of the set and expressing the property common to all the members.
So the above set may be written as
D={x|x∈N }
This is read as D is the set of all x such that x is a member of the natural number.
The symbol used for membership of a set. Thus a ∈ D means a is an element of D or a belongs to D.
c ∉ D means c does not belong to D or c is not a member of D.
Elements of a set can be people, cities, canals, oceans, or anything.
Some sets, along with their names are given below:-
N = The set of all natural numbers = {1,2,3,…}
W = The set of all whole numbers = {0,1,2,…}
Z = The set of all integers = {0,±1,+2…}.
Z ‘ = The set of all negative integers = {-1,-2,-3,…}.