Monday, February 9, 2009

I can prove to you that 2 = 1

a = b

a squared = a to the b power

a squared - b squared = ab - b squared

(a + b)(a - b) = b(a - b)

a + b = b

b + b = b

2b = 1b

2 = 1

This, my dear friends, is why I hate algebra. Can you blame me?


Art said...

Lol. How did you get your second premise? Is this a given, or your own conclusion from a=b?

The second premise doesn't follow logically from a=b. a squared = a*a = a*b, which clearly does not equal a to the b power.

The only instance where that would be true is if a=2.

I like algebra, but I don't blame you for hating it. =D

Hayley said...

If a is equivalent to b, then a to the power of b is definitely the same as a squared, because presumably all the terms are the same. You're right when you say, though, that the only instance where that could be true is if a=2. Because that's what a does end up equaling.

But I really have no idea. I copied this off the board in chemistry class. :P

M. Quigley said...

"Bogus" -Bill/Ted

Micah E. said...

No, if a is equivalent to b, than a * a = b * b... but that doesn't mean that a * a = a^b

If the second premise is true, b = 2, which means that a = 2, which means that... you lost me.

Hayley said...

I . . . will take your word for it. But come ON guys, that's not even the sneaky part of the simplification. What about this?

a = x

a+a = a+x [add a to both sides]

2a = a+x [a+a= 2a]

2a - 2x = a+x-2x [subtract 2x from both sides]

2(a-x) = a+x-2x [2a-2x= 2(a-x)]

2(a-x) = a-x [x-2x = -x]

2 = 1 [divide both sides by a-x]

Art said...

easy. Remember, a=x.
2(a-x)=a-x [from your problem]
2(0)= 0 [because any number minus itself is zero.]
It's impossible to divide by zero, so just multiply:


Hayley said...

Bravo! But you could also say that even though it's impossible to divide by zero, canceling terms is technically dividing, so while premise six is a little sneaky, it's technically possible. Math is fallible. Who knew?

Micah E. said...

It isn't impossible to divide by zero, you just end up with infinity every time you do.