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Pseudo-proof of that 2 = 1

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

a2   =   ab

a2 - b2   =   ab - b2

(a - b)(a + b)   =   b(a - b)

a + b   =   b

2b   =   1b

2   =   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.