Theorem: 1 = -1

Proof:

1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1


Also 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 = -1


As an alternative method for solving:


Theorem: 1 = -1

Proof:

x=1

x^2=x

x^2-1=x-1

(x+1)(x-1)=(x-1)

(x+1)=(x-1)/(x-1)

x+1=1

x=0

0=1

=> 0/0=1/1=1