Except that in your logic you're comparing two different terms. 2 and 1 in the expression 2=1 are of course the same term, both numbers with no variable.
But your situation is more like 2p = 1c (couple), and that makes sense, but that is not the same thing as saying 2=1.
So we don't want you 
Well, why should a+b= b if a = b?? I guess a/b would have to be zero, but even then it would be 0 = 0, not 2 = 1. So the wrong line should either be this one or the one before it, where this line came from.Yeah the 4th one makes no sense. why should a+b multiply the same thing as what b is multiplying if a+b is clearly a bigger thing to multiply than b? The line before it certainly doesn't justify that. Of course line 3 is absolutely correct, but it seems to do nothing to justify the 4th.
I'm not very far along in math but if:
a=b
then
a+b=b doesn't make sense, lets just assume a and b are both one because a=b.
so
1=1
1+1=1
Is that right, just close or completely wrong?
a = b
aa = ba
aa - bb = ba - bb
(a+b)(a-b) = b(a-b)
a+b = b
b+b = b
1+1 = 1
2 = 1
OK I copied your proof above so I can try again, I will just replace a & b with 1 to make it simple.
1=1 True
1x1=1x1 True
1x1-1x1=1x1-1x1 True
(1+1)(1-1)=1(1-1) True
1+1=1 False ( I think )
1+1=1 False again ( I think )
2=1 False according to general rules of math...
1=1 True
1x1=1x1 True
1x1-1x1=1x1-1x1 True
(1+1)(1-1)=1(1-1) True
1+1=1 False ( I think )
1+1=1 False again ( I think )
2=1 False according to general rules of math...
First, I didn't post the problem, but I sort of took it over since I often use this idea in class.
Second, there was a minor but important step left out (on purpose I believe).
(1+1)(1-1)=1(1-1) True
1+1=1 False ( I think )
Right here, to get from the first statement to the second, you need to divide both sides by (1-1), which is the division by zero I was referring to. And you are right, it is false because you cannot divide by zero and get a meaningful answer. Just try it with your calculator, it will have fits. It is a little more obvious here, not as much when it is in the a-b form.
I'm kinda getting confused
So the flaw is that to get from step 1. to step 2. you have to divide by zero and division by zero is impossible so that is the flaw?
It all makes sense now!
the reasoning is that something plus itself equals itself, and whenever you work anything with itself it will always be itself (srry if this is confusing). but this is only possible with 0, also known as a and b in this problem.
An old one, but for those who haven't seen it before: What's wrong with the following reasoning?
a = b
aa = ba
aa - bb = ba - bb
(a+b)(a-b) = b(a-b)
a+b = b
WHOA! Hold on there princess, you can't just cancel out the (a-b) on both sides, that's division by 0. Nice try.
b+b = b
1+1 = 1
2 = 1
By the way, someone should convince erik to implement LaTeX support in these forums :/
A more general statement (or why you can not divide by zero)
0.a=0.b for all a and b (This is true but you still have to prove it)
If we permit division by zero then
a=b for all a and b.
I thought it might be confusing to introduce two symbols a and b and then write a=b. I do appreciate you wanted to hide the flaw and that was the point of the exercise.
a=b --> (a-b) = 0 --> (a-b)/(a-b) = Error