Note: This item is one of a special case - Known Unknowables
An irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction.
Examples are π, √2 etc.
For many irrational numbers, relatively simple mathematical proofs exist which show that it's impossible to ever arrive at finite solution.
(√2 was proved to be an irrational number by Greek mathematicians more than 2000 yrs ago).