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 = a^{2} = a^{2} - b^{2} = (a - b)(a + b) = a + b = 2b = 2 = |
b ab^{ } ab - b^{2} b(a - b) b 1b 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 being synonymous.