What is wrong with the following calculations that seem to prove that 2 equals 1?
a = b let a = b aa = ab multiply by a aa - bb = ab - bb subtract bb (a + b)(a - b) = b(a - b) factor out a + b = b divide by (a - b) 2a = a substitute a for b 2 = 1 divide by a
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The Answer:
The reason this seems to work is because we attempt to divide by zero.
a = b means that aa = bb = ab, so when we:
aa - bb = ab - bb subtract bb we actually end up with:
0 = 0 Then when we factor out another zero (a-b) we are actually dividing by zero:
(a + b)(a - b) = b(a - b) factor out zero (a-b) Which is an illegal operation.
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Last updated October 10th, 2003