What is Countability in Set Theory?

Countability is a property of sets that states that the set can be put into a one-to-one correspondence with the natural numbers. In other words, if we can pair each element of the set with a unique natural number, then the set is countable.

For example, the set of all natural numbers is countable because we can pair each natural number with a unique integer. The set of all rational numbers is also countable for the same reason. On the other hand, the set of all real numbers is not countable because there are uncountably many real numbers and there is no way to pair each real number with a unique natural number.

I like this

I dislike this

Report a content error

Share

Report a content error

Thank you! Your form was successfully submitted.

We apologize! Your form could not be submitted. Please try again later.

Submit reports

Share

• 
• 
• 
• 
• 
• 
• 
• 
•