Proof by contradiction that $\sqrt{2}$ is irrational, why assume the fraction is simplified?

68 Views Asked by At

As a student with no history of proof-based math courses, I am having some difficulty understanding the proof by contradiction by assuming $\sqrt{2} = a/b$ and that a and b are in least common denominators.

Could you explain how this disproves that it is irrational? Doesn't it just merely disprove that our initial assumption that a and b are even, is wrong?

I'm speaking of the popular proof that is given here:https://www.math.utah.edu/~pa/math/q1.html