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Algebraic Paradox?

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To be archived: Can anyone understand this?

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By Carl Evans on Friday, October 12, 2001 - 12:24 am:

a = b
ab = b²
-(ab) = -b²
a²-ab = a²-b²
a(a-b) = (a+b)(a-b)
a = a+b
a = 2a
1 = 2

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By Sam Davies on Friday, October 12, 2001 - 12:47 am:

There is a problem going from the 5th line to the 6th. The fifth is true, a(a-b) = (a+b)(a-b), but a = b (original definition) therefore a-b = 0.

So to get from the fifth line to the sixth you divide both sides by (a-b), i.e. divide by 0 - not allowed. Therefore 1¹2.

Hope this makes sense

sam

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