1=2?

[KMR]

An interesting problem my friend showed me 0=0x-x = x-xx^2 - x^2 = x^2 - x^2(x+x)(x-x)=x(x-x)Both sides have '(x-x)'(x+x)=x2x=x2=1Proof x^2 - x^2=(x+x)(x-x)(x+x)(x-x)=0x^2 + x^2 - x^2 - x^2 [Expanding Brackets]LHS=RHSso (x+x)(x-x)=0=x^2 - x^2Someone please explain.

 

[ksdhart]

That long list of things which are supposedly equal is totally invalid. It starts off with 0 = 0x - x = (something else). But already we can see that it's only true if x = 0. And because x is 0, the whole thing evaluates out to 0 = 0 = 0 = 0 = 0.