Watch closely: I will prove that 2 = 1. Your job is to show why such a logical proof could possibly be wrong. It isn't sufficient to point out that the answer is ridiculous.
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a = a2 = a2 - b2 = (a - b)(a + b) = a + b = 2b = 2 = |
b ab ab - b2 b(a - b) b 1b 1 |
definition multiply both sides by a subtract b2 factor cancel like factors* since a = b divide by b |
* Note:
A kind reader, Michael Cole, pointed out that factors are multiplied, while terms are added, correcting my earlier (rather sloppy) treatment of them as synonymous.