[extropy-chat] Tyranny in place

[Samantha Atkins]

x = y  => (x-y) = 0  so division by zero is being done when dividing  
by (x - y)
x + y = y  => x = 0

On Oct 3, 2006, at 11:28 AM, nvitamore at austin.rr.com wrote:

>
> From: Eliezer S. Yudkowsky
>
>> spike wrote:
>>> This is a paradox that we cannot solve with our usual tools.   
>>> Logic simply
>>> fails.
>
>> Heinlein had a sympathetic character say, in one of his stories:   
>> "Logic
>> is a fine thing, but I have seen a perfectly logical proof that 2 =  
>> 1."
>> (If anyone remembers which story this is from, please let me know.)
>
>> Heinlein was probably thinking of this:
>> x = y = 1
>> x = y
>> x^2 = xy
>> x^2 - y^2 = xy - y^2
>> (x+y)(x-y) = y(x-y)
>> x+y = y
>> 2 = 1
>
> Proof that 2 equals 1
>
> 1) Given:
>   X=Y
> 2) Multiply both sides by X:
>   X^2=XY
> 3) Subtract Y^2 from both sides:
>   X^2-Y^2=XY-Y^2
> 4) Factorise:
>   (X+Y)(X-Y)=Y(X-Y)
> 5) Cancel out (X-Y) term:
>   X+Y=Y
> 6) Substitute X for Y, by equation 1
>   2Y=Y
> 7)Divide both sides by Y
>   2=1
>
>   — "Omni"
>
> Natasha
>
>
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