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Old 11-15-2005, 12:42 AM   #1
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Exclamation 1 = 2

Assume that A = B.

AČ = AB
AČ - BČ = AB - BČ
(A + B)(A - B) = B(A - B)
A + B = B
B + B = B
2B = B
2 = 1

And there you have it! One is equal to two.

Your goal? Find the error in the proof. First to find it gets a big bear hug from a mushroom.
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Old 11-15-2005, 07:18 AM   #2
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Default Re: 1 = 2

2b=b
- -
2 2

B=1
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Old 11-15-2005, 07:52 AM   #3
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Default Re: 1 = 2

god it 2 late :S i'm saying that 2= Cat X Mushroom all divided by a pony
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Old 11-15-2005, 08:17 AM   #4
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Default Re: 1 = 2

Quote:
Originally Posted by lhuser
2b=b
- -
2 2

B=1
You're going to have to explain that.... not sure what you're trying to say.
Quote:
Originally Posted by AOD
god it 2 late :S i'm saying that 2= Cat X Mushroom all divided by a pony
Close.
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Old 11-15-2005, 08:27 AM   #5
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Default Re: 1 = 2

(A + B)(A - B) = B(A - B)

Here's where you start to go wrong.

The equation above equates to:

A^2 - AB + BA - B^2 = BA - B^2

=> BA - B^2 = 0
=> BA = B^2
=> B x A = B x B
=> A = B

where ^ is "to the power of".

I think you have to multiply out the brackets before simplifying your answer.

OR if you don't assume that A=B, the same equation equates to:

=>A^2 - AB = 0
=>A^2 = AB
=>A x A = A x B
=>A = B
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Old 11-15-2005, 09:21 AM   #6
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Default Re: 1 = 2

Quote:
Originally Posted by lhuser
2b=b
- -
2 2

B=1
Thats quite clear, you can't just divide b out of each side, you can only divide the number, thus it's completly screwed. Plus I dought A^2 = AB is hardly proven. Because if A was squared it would = a number, lets say:
A=2 B/=A (cannot equal) because if it was equal, it would also be considered A^2, so each side cannot equal each other from the start.
(starts to think...) unless:
A^2 = AB

(A^2)/A = (AB)/A
A=B :P
Meh it's certainly a f**ked up equation.


Chris
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Old 11-15-2005, 01:36 PM   #7
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Default Re: 1 = 2

Quote:
Originally Posted by CJ
The equation above equates to:

(1)A^2 - AB + BA - B^2 = BA - B^2

(2)=> BA - B^2 = 0
(3)=> BA = B^2
(4)=> B x A = B x B
(5)=> A = B

where ^ is "to the power of".

I think you have to multiply out the brackets before simplifying your answer.

OR if you don't assume that A=B, the same equation equates to:

=>A^2 - AB = 0
=>A^2 = AB
=>A x A = A x B
=>A = B
Step 1 is correct making it equal to the line before it:

AČ - BČ = AB - BČ

So to separate it into "(A + B)(A - B) = B(A - B)" is valid.

Your following steps (2-5) are also valid, but they don't make the proof untrue. It still works, as you can see, but you're getting warm.
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Old 11-15-2005, 01:45 PM   #8
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Default Re: 1 = 2

Quote:
Originally Posted by draconum
Thats quite clear, you can't just divide b out of each side, you can only divide the number, thus it's completly screwed. Plus I dought A^2 = AB is hardly proven. Because if A was squared it would = a number, lets say:
A=2 B/=A (cannot equal) because if it was equal, it would also be considered A^2, so each side cannot equal each other from the start.
(starts to think...) unless:
A^2 = AB

(A^2)/A = (AB)/A
A=B :P
Meh it's certainly a f**ked up equation.


Chris
I think you're confusing your algebra a bit. It's perfectly legal to divide B from both sides of the equation:

2B = B
2 = 1

The B variable cancels from both sides. Think about it as if B were a number. In fact, B is a number, we just don't know which one.

Also, AČ is equal to AB since we already know that A is equal to B.

Original equality:
AČ = AB
Expanded equality:
AA = AB
Cancel the A's:
A = B

This returns our already stated assumption therefore validating the procedure. Also, when you say that AB would be considered to be AČ, that's exactly what I'm saying when I set AČ equal to AB. You sort of proved that step to yourself in your question.
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Old 11-15-2005, 04:26 PM   #9
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Default Re: 1 = 2

How complicated can this thread get!
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Old 11-15-2005, 06:53 PM   #10
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Default Re: 1 = 2

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