On: Euclid's Proof that √2 is Irrational

[DiggyJohnson]

Even x Even results Even

Even x Odd irrelevant if squaring

Odd x Odd results Odd

[bsaul → DiggyJohnson]

except sqrt(2) x sqrt(2) is even ( i know we're talking about numbers in Z in this case, and sqrt(2) definitely isn't in Z, but still)

Which made me wonder if the original sentence isn't already assuming something about sqrt(2) and even/odd properties.

(i stopped at the same step as OP wondering if this is as trivial as it seemed)

[lIl-IIIl → DiggyJohnson]

>Odd x Odd results Odd

This isn't obvious and can't be taken for granted. The explanation posted above (2k+1)^2 by Smaug123 explains this part.