HOW TO PROVE THAT 2 = 1

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A student was given an assignment to show that 2 = 1. He successfully showed this using the argument below.

PROOF

Let a, b be real numbers, such that

a = b = 1  

Then,

a^2 = ab

a^2 - b^2 = ab - b^2

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

This imply,

(a+b) = b

Since a=b=1

Hence,

2 = 1   QED.

 

An alternative proof is;

For any x real number,

x^2 = x^2

x^2 - x^2 = x^2 -x^2

x(x - x) = (x -x)(x + x)

This imply

x = x + x

x = 2x

Hence, 1 = 2  QED.

 

REMARK 

There is something wrong with these proofs. kindly spot out the line where the argument has a flaw.