every two rational numbers have a rational number between each other.
q, p are rational
(q + p) / 2 = r
r is rational
if sqrt(2) is not rational then it absolutely cannot be surrounded by two rational numbers.
sqrt(1), sqrt(2), sqrt(4) -> 1, sqrt(2), 2
clearly it is surrounded by two rationals at any time.
sqrt(2) must be rational.
there is no point in reals, it's completely fucking retarded.