"x is rational" means there are two integers p,q such that x=p/q. So for example, 2/3 is rational (p=2, q=3), but the square root of 2 is not rational (there i

"x is rational" means there are two integers p,q such that x=p/q. So for example, 2/3 is rational (p=2, q=3), but the square root of 2 is not rational (there is no such fraction). The last part is not very obvious (it greatly distressed the Pythagoreans when they figured it out) but there are a bunch of proofs in Wikipedia: https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irrationality https://en.wikipedia.org/wiki/Square_root_of_2#Proofs_of_irr...