# 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

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#### 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. RAMEEZ AHMAD says:

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. s.m.faraz says:

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. jignesh says:

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

1. RAMEEZ AHMAD says:

yeh really

4. jignesh says:

your ans is wrong becous ” a = x ” so and so (a-x = 0) and we can’t divide by it…

5. Nisarg says:

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.

6. abhiron bhattacharya says:

in both the proofs ur diving both sides by quantities equalling to zero i.e—(a-x) & (a-b)

7. well i am a science maths student and even then couldn’t get the trick. i plan to try this on our institute teacher let’s see if it works………well this is cool

8. SHIVAM says:

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

9. jeswin vinod says:

dear brother
to subtract a nummber ffrom two addition numbers
we wnat to put the bracket
(a+x)-2x

10. arun chakravarthi says:

rocking

11. GVS Siva Kumar says:

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

12. Saurabh Pathak says:

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

13. Saurabh Pathak says:

in proof 1st :
dividing by (a-x) is not justifiable as “a=x” which means (a-x)=0

14. karthik says:

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.

15. 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.

16. Nikhil says:

Too Good. I like such proofs. Thanks to this site.

1. Ashok says:

you dont know about the maths please read its basic and then comments