proof of 2=1

[perkeyone]

i learned this in my ap calculus ab class
there is a flaw in the equation but it is still kinda neat to me
i will tell you guys the flaw later so that some of you can try to figure it out on your own
here goes...

...............equation :": reason

.............a=b.........:": given (a not equal to 0)
.........a^2=ab........:": multiplication property of equality
..a^2-b^2=ab-b^2.:": subtraction property of equality
(a-b)(a+b)=b(a-b)...:": factoring
.........a+b=b..........:": division property of equality
.........b+b=b..........:": substitution
...........2b=b..........:": simplify
............2=1...........:": division property of equality