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

[Prime8]

Re: proof of 2=1

You can't divide by (a-b) because that is equal to 0. If a=b, then a-b=0, and you can't divide by 0. I learned this too last year in my Calculus AB class, but I also learned another way involving square roots and imaginary numbers.

[MrRubix]

Re: proof of 2=1

Division property of equality doesn't hold here since a=b so you're dividing by 0. Everyone probably knows the "trick" to this one by now, unfortunately.

[perkeyone]

Re: proof of 2=1

i didnt get to edit it in time to say not to post the answer... oh well

[Prime8]

Re: proof of 2=1

Sorry about ruining it. I thought you were asking if any of us COULD figure it out. Here's the other one I learned. This one too is fallacious, but I'll leave it to you guys to find where it is wrong.


Let's start off with two versions of -1 equal to each other:
1/-1 = -1/1

Now, we'll take the square root of both sides:
SQRT(1/-1) = SQRT(-1/1)

Now, let's simplify this:
SQRT(1)/SQRT(-1) = SQRT(-1)/SQRT(1)

Again, to further simplify this. Also, we'll substitute i for SQRT(-1):
1/i = i/1

Now, we'll divide each side by 2:
1/2i = i/2

Now, let's add (3/2i) to each side of the equation:
(1/2i) + (3/2i) = (i/2) + (3/2i)

Now, we'll multiply both sides by i:
i{(1/2i) + (3/2i)} = i{(i/2) + (3/2i)}

Now, let's substitute that i into the equation:
(i/2i) + (3i/2i) = (i^2/2) + (3i/2i)

Now, we'll simplify the equation once again. Know that i/i is 1 and i^2 is -1:
1/2 + 3/2 = -1/2 + 3/2

This leads us to our final equation:
2 = 1

[Squeek]

Re: proof of 2=1

Old and not worthy of Critical Thinking.