Question

Are there more rational numbers than irrational numbers?

Answer 1

Comparison of irrational numbers than rational numbers:

No, there are more irrational numbers than rational numbers.

Explanation:

Rational numbers are the numbers which can be expressed in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$. They can be put in one to one correspondence with the natural number so they are countably finite. There are more irrational numbers between two rational numbers than there are rational numbers between two irrational numbers. There exist an infinite number of irrational numbers between a single pair of rational numbers, $1$ and $2$.We cannot even assign an order among irrational numbers. Hence, the irrational numbers are countably infinite.

Hence, there more irrational numbers than rational numbers.