What are Countable Sets and Uncountable Sets? Give some examples.
A set is countable if: 1) It is finite, 2) It is made of one to one correspondence with Naturals N. called countably infinite.
The set which does not hold one to one correspondence with Natural Numbers N is called Uncountable Set.
Updated: Aug 20, 2024, 15:53 IST
COUNTABLE SETS:
A set is countable if: 1) It is finite, 2) It is made of one to one correspondence with Naturals N. called countably infinite.
It means that there exist a bijection from N to that set.
For example, take a set S
Then, S is countable if either S is finite or N ~ S.
Some examples of countable sets are:
• {1,2,3,4,5}
• {-3,-2,-1,0,1,2,3}
• {….-3,-2,-1,0,1,2,3….} = Integers Z
• Rational Numbers Q
• Natural Numbers N
• Even Numbers
• Odd Numbers
• Whole Numbers W
• Positive Integers
• Negative Integers, etc
UNCOUNTABLE SETS:
The sets which are not countable are known as uncountable sets. It means that the set which does not hold one to one correspondence with Natural Numbers N is called Uncountable Set.
Some examples of uncountable sets are:
• Irrational Numbers
• Real Numbers R
• Complex Numbers C
• All intervals example- (1,2) ; [5,9) ; (0.5,1) etc.