x,y are in R. Suppose x2+y2=0. Prove that x=0 and y=0. My proof: Suppose x[itex]\neq[/itex]0, y[itex]\neq[/itex]0. Then by the field axioms, both x2 and y2 are strictly positive, and so is their sum. This is a contradiction, since we supposed that their sum = 0. Thus, x=0, and y=0. This problem and proof seem so simple, I think there may be something wrong with it.