Firstly, one would assume that we have to take a2 to be a^2 here (i.e. a to
the power 2).
So we have,
1. a = a
2. a^2 = a^2
3. a^2 - a^2 = a^2 - a^2
4. (a+a)*(a-a) = a*a - a^2
5. (a+a)*(a-a) = a*(a-a)
6. (a+a) = a
7. 2a = a
8. 2 = 1
Looking at line 5 we essentially have (a+a)*0 = a*0, and then we remove the
common factor of zero from each side [the (a-a)]; i.e. division by zero.
This kills the proof.
Michael Cartwright
----- Original Message -----
From: "Sharpe, Alan D" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Monday, 28 January, 2002 16:22
Subject: question: 2=1?
> I recently saw this proof, and cannot work out what is going on.
>
> a = a
> a2= a2
> a2 - a2 = a2 - a2
> (a + a)*(a - a) = a*a - a2
> (a + a)*(a - a) = a*(a - a)
> (a + a) = a
> 2a = a
> 2 = 1 ?
>
>
> does anybody have an explanation
>
> Cheers
> alan sharpe
>
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