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Introduction to Sets and Their Types
Sep 8, 2024
Notes on Sets
Definition of Set
A set is a
well-defined collection
that contains different
objects
.
A set is always denoted by
capital letters
(like A, B) and written in
curly brackets
.
Characteristics of Set
A set must be
well-defined
.
Example:
If we ask "Who are the top 5 cricketers in India?" the answers may vary.
But if we ask "What are the natural numbers less than 10?" the answer will always be from 1 to 9.
Types of Sets
Empty Set
It contains no elements.
It is represented by
or
{}.
Example: x is an even number greater than 2.
Finite Set
It has a countable number of elements.
Example: {1, 2, 3, 4, 5, 6} (This is a set of 6 elements).
Infinite Set
It has uncountable elements.
Example: the set of natural numbers.
Like {1, 2, 3, ...}.
Singleton Set
It contains only one element.
Example: {1} or {2}.
Equal Set
When two sets have the same elements, they are said to be equal.
Example:
A = {1, 2, 3, 4}
B = {3, 4, 1, 2}
C = {2, 1, 3, 4}
All have the same elements, so A = B = C.
Conclusion
Today we learned about sets and their various types.
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