# Thread: Disprove proof of 2=1

1. ## Disprove proof of 2=1

Here is what the teacher has given us:

a=b for some a, some b
a+a=a+b (add a to both sides)
2a=a+b
2a-2b=a+b-2b (subtract 2b from oth sides)
2(a-b)=a+b-2b [2a-2b=2(a-b)]
2(a-b)=a-b
2+ 1 (divide by a-b)

One step here is wrong, or so the teacher says. Which one is it?

2. a=b for some a, some b
a+a=a+b (add a to both sides)
2a=a+b
2a-2b=a+b-2b (subtract 2b from oth sides)
2(a-b)=a+b-2b [2a-2b=2(a-b)]
2(a-b)=a-b
2 = 1 (divide by a-b)

One step here is wrong, or so the teacher says. Which one is it?
The last step, the division by (a-b).

You said a=b at the beginning. If that is so, then a-b = 0.
Hence, since you cannot divide by zero, then the last step is wrong.

3. Wow, thanks, that's absolutely right! I can't believe I overlooked that. Thanks!