Proof That The Square Root Of Two Is Irrational.

Here is a proof that √2 cannot be written as a fraction and hence is irrational:

• Every rational has a reduced form.
• A reduced form cannot have two evens.
• Every square of an odd is an odd.
• Every square of an even is an even.
• If m / n is the reduced form of √2, then m² = 2n².
• That implies m² is even.
• That implies m is even.
• That implies m = 2k for some integer k.
• That implies n² = 2k² for some integer k.
• That implies n² is even.
• That implies n is even.
• m and n cannot both be even.
• m / n does not exist.
• √2 cannot be written as a fraction.
• QED