Proof that 2=1

[amykhar]

Let a = b

a squared = ab
a squared - b squared = ab - b squared
(a+b)(a-b) = b(a -b)
a+b = b
2b = b (because a=b)
2 = 1

Now, I know why this proof is bogus. Do you?

[mrisch[$]]

I do, but I won't give it away.

[amykhar]

I just gave this to two people at work - an engineer and a liberal arts person. Guess who got it first?

[nc10]

amykhar said

I just gave this to two people at work - an engineer and a liberal arts person. Guess who got it first?

I get it, as an engineer, I sure hope your engineer got...

[conradd]

amykhar said

Now, I know why this proof is bogus. Do you?

Because 2B is not 2B

Deb
channeling Hamlet's math teacher

[jenninca]

Ugh, that takes me back to my days in Geometry class and there's no way I want to go back to those!

Cindy
who did not do so well in geometry

[lynnzop[$]]

amykhar said

Now, I know why this proof is bogus. Do you?

Nope.

That's why God created accountants.

Lynn
liberal arts major who blanks out at any indication of math problems

[emeleel]

Makes me think of that T-shirt:

"To be is to do"
"To do is to be"
"Do be do be do"

[theworm[$]]

I majored in art, but scored well on on the logic tests.
I know why this isn't valid! It's obvious.
Except it seems so obvious that I'm doubting if I'm right.

But, I am right.

[amykhar]

The liberal arts reporter girl-child got it before the MIT engineer. I gave it to her to look at because she's going to Columbia for graduate school in two months. Told her she couldn't leave until she passed my test

The problem with the proof happens when you go from this step:

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

To this one:
a+b = b

Think about all the rules you know about division, and that should be enough of a hint for you.

Amy

[amykhar]

p.s. My cab driver last night gave me this little proof to play with. He has a degree in economics and we had a nice ride back to the paper talking about topology of all things.

[Redlass]

I think I have it.

[theworm[$]]

I always like algebra. Never could get calculus, but I like algebra. It was always like a number puzzle. It's my geek gene.

[CurtisEdmonds]

amykhar said

The liberal arts reporter girl-child got it before the engineer. I gave it to her to look at because she's going to Columbia for graduate school in two months. Told her she couldn't leave until she passed my test

The problem with the proof happens when you go from this step:

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

To this one:
a+b = b

Think about all the rules you know about division, and that should be enough of a hint for you.

Amy

Actually, it's the step before that's the problem, and it's a multiplication rule. The next step just makes it worse.

[theworm[$]]

Oh, ok! I just pmd you because I thought the problem was more simple and earlier. Curtis seems to be validating me. Sad that I still need external validation, huh?

[mrisch[$]]

No, it's not earlier, because in that step no mathematical rules have been violated.

[theworm[$]]

Yeah, I get it now. That's where it stops moving to the 1=2, but the "rule" wasn't broken until later.

[Flamepillar]

This kind of reminds me of the proof that .9999999999~ = 1. The ~ symbol means the 9's go on forever, like when you put the little line over it

let x = .999999999~

so 10x = 9.9999999999999~

10x - x = 9x

9.9999999999~
-.99999999999~
==========
9

so 9x = 9

so x=1

Or something like that :p

[Helen_B[$]]

Wormie, we're always glad to validate you.

[Penguinlady[$]]

My eyeballs start spinning in opposite directions and I break out in a cold sweat when math problems heave - literally! - into view. So I have no idea where the problem is. But I feel as though I'm sipping tea with the Mad Hatter.