(1) | = P/Q. | Assume is rational. |
(2) | GCD(P,Q)=1 | P/Q is expressed in lowest terms |
(3) | Q2 = 2感2 | Square both sides & multiply by Q2 |
(4) | Q = 2愛 | Both sides must be divisible by 2 |
(5) | (2愛)2 = 2感2 | Substituting |
(6) | 4愛2 = 2感2 | Expanding |
(7) | 2愛2 = P2 | Divide both sides by 2. |
(8) | P = 2惹 | Both sides must be divisible by 2. |
(9) | GCD(P,Q)=2 | Both P and Q divisible by 2. |
(10) | P/Q | By reductio cannot be rational. |