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

Vineet Patawari

Hi, I'm Vineet Patawari. I fell in love with numbers after being scared of them for quite some time. Now, I'm here to make you feel comfortable with numbers and help you get rid of Math Phobia!

18 thoughts to “Is two equals one?”

  1. Playing ways……..which forces U to think more & more………………..thankx to make me anxious to find it out that
    1=2? By any other method

  2. now i will give another proof that u cant neglect…….
    we know
    -2=-2
    4-6=1-3
    4-6+(9/4)=1-3+(9/4) [adding 9/4 on both sides]
    [2-(3/2)]^2=[1-(3/2)]^2 [by using (a-b)^2]
    2-(3/2)=1-(3/2) [square root on both sides]
    2=1 hence proved

  3. in proof 2nd also :
    dividing by (a-b) is not justifiable as “a=b”

    (a+b)(a-b) = b(a-b) [dividing both sides by (a-b)
    it is wrong

  4. a-b is divided which is equal to 0. In mathematics number divided by 0 is undefined. This equation cannot go further after step 4.

  5. WHAT EXACTLY YOU ARE DOING IS THAT YOU ARE MULTIPLYING A QUANTITY WITH ZERO AND THEN CANCELING OUT THE ZERO WHICH IS RUBBISH

  6. Division by ZERO is not defined.
    In the above two ways of proof division is done by ZERO.
    Hence the proof is false.

  7. Basic RUle:when u divide a equation both side by some number,it should not be ZERO.
    In d first proof ur dividing both side by (a-x),so that means a is not equal to x,but ur 1st assumption is that a=x.
    and in d same way in the second proof,ur dividing with (a-b),so that impies a should not be equal to b,but in the very next step ur using the condition a=b.

  8. You can’t divide a number by zero. In this proof a is made equal to b and then division is carried out by (a-b) which is just another way of dividing by zero and thus is not permissible in mathematics.

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