- #1

ViolentCorpse

- 190

- 1

There's something I don't understand in the popular "proof by contradiction" of sqrt(2) after the following step:

a

^{2}/b

^{2}= 2

a

^{2}=2b

^{2}

The above equation implies that a

^{2}is even. Fair enough. But the way I see it, the above equation also makes it impossible for a to be even, as

a=sqrt(2)*b.

This implies that a should actually be an irrational number as it is a multiple of sqrt(2). Though it seems obvious to me that if some number n^2 is even, then n must also be even, but in the context of the equation a

^{2}=2b

^{2}, it doesn't seem possible.

Shouldn't this be the end of the proof? We started by assuming that a and b are whole numbers and a/b can be used to represent sqrt(2), but found that a, at least, is actually irrational. Doesn't that count as a contradiction?

I'm really confused. :(