Originally posted by Liberalkid: Your proof is fallacious, due to division by zero. I'll break it down.
a+b=c a+b-c=0 4*(0)=3*(0) So when you "remove the same term left and right" you're diving both sides by zero. But you can't divide both sides by zero, because division by zero is undefined.
Before you say something about math not understanding division by zero, we could very easily define a number system where division by zero is defined (the properties of the real numbers just break down then). It's a concious decision to make division by zero undefined.