# Puzzles & Games Proof that 2 = 1 - solved

Discussion in 'Puzzles & Games' started by kiwirobin, Feb 14, 2005.

1. ### kiwirobinPremium Member

A Proof That 2 = 1

Given
(1) X = Y

Multiply both sides by X
(2) X^2 = XY

Subtract Y^2 from both sides
(3) X^2 - Y^2 = XY - Y^2

Factor both sides
(4) (X+Y)(X-Y) = Y(X-Y)

Cancel out common factors
(5) (X+Y) = Y

Substitute in from line (1)
(6) Y+Y = Y

Collect the Y's
(7) 2Y = Y

Divide both sides by Y
(8) 2 = 1

Q: What's wrong with this 'proof'?

[Edited on 2-16-2005 by kiwirobin]

2. ### junior_smithPremium Member

whya re you adding and subtractnig variables because i could do that with anything and make it equal to any number

3. ### kiwirobinPremium Member

Ok the j_s then answer the question.
Show me the flaw in the proof!!

4. ### IcewolfPremium Member

The only way that this will work out is if,
x = y = 0

Which leads to the point that zero obejects cannot be divided into zero groups. (if you want a more detailed answer I can give you it)

5. ### kiwirobinPremium Member

This is also correct ice but the challange was to solve this problem.

Q: What's wrong with -THIS- 'proof'?

Where is the application that is not correct.

6. ### IcewolfPremium Member

Part 5, cancel out means divide, if we say
x = 0
y = 0
therefore x - y = 0

therefore you are dividing by 0 which is not allowed

[Edited on 16-2-2005 by Icewolf]

7. ### kiwirobinPremium Member

That's it ice
Took me ages to find it, funny how my brain can only vocus on one thing sometimes exclueding the obvious.
For a while there I was starting to believe it...:mnky:

anyway, well done...
here's the breakdown for those interested...

2 = 1: Solution
'Cancelling' the common factors from line (4) to (5) means dividing by the factor (X-Y). Since X=Y, this is a division by 0, the results of which are undefined.

(1) X = Y Given
(2) X^2 = XY Multiply both sides by X
(3) X^2 - Y^2 = XY - Y^2 Subtract Y^2 from both sides
(4) (X+Y)(X-Y) = Y(X-Y) Factor both sides
(5) (X+Y) = Y Cancel out common factors
(6) Y+Y = Y Substitute in from line (1)
(7) 2Y = Y Collect the Y's
(8) 2 = 1 Divide both sides by Y