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.
a = b a^{2} = ab a^{2} - b^{2} = ab - b^{2} (a - b)(a + b) = b(a - b) a + b = b 2b = 1b 2 = 1 |
definition multiply both sides by a subtract b^{2} 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.