Irrational number

There are an infinite number of rational numbers, but there are infinitely more irrational numbers. Neither type of number can represent every type of numeric quantity. By combining the rational and irrational numbers into the real numbers, a continuum of numbers is created which can represent any quantity in


Although the Greeks initially thought all numeric qualities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this?