Finite sets:
Consider the following sets
A = { a, b, c }
B = Set of alphabets in English language
C = Set of days in a week
D = Set of solutions of the quadratic equation x2- 5x + 6 = 0
E = Number of men in a party
As we examine set A, it has 3 elements.
As we examine set B, it has 26 elements.
As we examine set C, it has 7 elements.
As we examine set D, it has 2 elements.
As we examine set E, it may contain nay finite number of elements.
We could write number of elements of a set A as n(A)
So, Following the above sets we have
n(A) = 3
n(B) = 26
n(C) = 7
n(D) = 2
n(E) = any natural number.
Finite Sets Definition
As we could count the number of elements in a set, it is called as finite set.
An empty set is also a finite set.
If n(S) = a natural number, then S is a non- empty finite set.
Infinite Sets
Consider the set of all natural numbers
We know that natural numbers start with 1 and has no ending number.
N = { 1, 2, 3, ... }
In such case, can we count the number of elements in the set ?
No !
Such sets are called as infinite sets.
Some more examples:
Set of even natural numbers
{ 2, 4, 6, 8, ...}
Set of integers
{ ..., -3, -2, -1, 0, 1, 2, 3, ... }
Set of prime numbers
{ 2, 3, 5, 7, ...}
Set of real numbers
State whether each of the following sets are Finite or Infinite:
- The set of lines parallel to y axis
- Set of numbers which are multiple of 5
- Set of circles passing through teh origin (0,0)
- E = {0}
- H = {}
- Infinite
- Infinite
- Infinite
- Finite
- Finite