Is two equals one?

Is 2 = 1?

Today, I will prove that two is equal to one (2 = 1). I will do that in more than one way.  You know what you have to do? You have to point out the fallacy in the proofs.

The Fallacious Proof – 1:

Let,  a = x

a+a = a+x          [add a to both sides]

2a = a+x          [a+a = 2a]

2a-2x = a+x-2x       [subtract 2x from both sides]

2(a-x) = a+x-2x       [2a-2x = 2(a-x)]

2(a-x) = a-x          [x-2x = -x]

2 = 1            [divide both sides by a-x]

Hence Proved

The Fallacious Proof – 2:

Let,  a = b

a^2 = ab     [multiplying ‘a’ both sides]

a^2 – b^2 = ab – b^2   [subtracting b^2 from both sides]

(a+b)(a-b) = b(a-b)      [dividing both sides by (a-b)]

a+b = b

b+b = b    [since a=b, replacing a by b]

2b = b

2 = 1 [dividing both sides by b]

Hence Proved

18 Comments
  1. RAMEEZ AHMAD
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