actually, if a=1 and b=1, then a=b, so dividing by a-b is dividing by zero. You can't divide by zero which is the fundamental flaw in that proof
About 1+1=2. I thought that it was just that by definition. We just define our set of numbers (starting at 0) as 0, 1, 2, 3, 4... etc. Two is one...