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‘Proof’ that 2 = 1

let a = b, then a^{2} = ab

a^{2} - b^{2} = ab-b^{2}

(a-b)(a+b) = b(a-b)

a+b = b, substituting gives b+b = b

2b = b therefore 2 = 1

Where is the error made?

let a = b

then a^{2} = ab

a+b = b

substituting b+b = b

2b = b

2 = 1

You need to be aware that a – b = 0. This false proof relies on dividing both sides of an equation by zero which should not be done.

Yes