# Prove that the set of irrational numbers in [0,1] is not countable

Prove that the set of irrational numbers in [0,1] is not countable
You can still ask an expert for help

## Want to know more about Irrational numbers?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

faldduE
It is known that the set of rational numbers are countable.
Union of rational numbers and irrational numbers gives the real numbers.
So $\left[0,1\right]=Q\left[0,1\right]\cup RQ\left[0,1\right]$
Since Q[0,1] is countable and [0,1] is not countable.
So the only possibility is that $RQ\left[0,1\right]$ is uncountable.
Hence, the set of irrational numbers in [0,1] is not countable.