# 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.