## 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**

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

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

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

yeh really

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

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.

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

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

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

dear brother

to subtract a nummber ffrom two addition numbers

we wnat to put the bracket

(a+x)-2x

rocking

Division by ZERO is not defined.

In the above two ways of proof division is done by ZERO.

Hence the proof is false.

in proof 2nd also :

dividing by (a-b) is not justifiable as “a=b”

in proof 1st :

dividing by (a-x) is not justifiable as “a=x” which means (a-x)=0

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.

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.

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

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