|Theorem: 1 = -1Proof:1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1Also one can disprove the axiom that things equal to the same thing are equal to each other.1 = sqrt(1)-1 = sqrt(1)Therefore 1 = -1As an alternative method for solving:Theorem: 1 = -1Proof:x=1x^2=xx^2-1=x-1(x+1)(x-1)=(x-1)(x+1)=(x-1)/(x-1)x+1=1x=00=1=> 0/0=1/1=1