Is it possible for 2 = 1???

Question

Let's take x = y.

x = y

We multiply both sides by x to get:

x^2 = xy

We subtract y^2 from both sides to get:

x^2-y^2 = xy-y^2

After factorising both sides, we get:

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

If we divide (x-y) from both sides:

(x+y) = y

If x = y:

2y = y

Divide by y:

2 = 1

Why?

Answer 1

Proof that 2 equals 1

* Let a and b be equal non-zero quantities

a = b

* Multiply through by a

a2 = ab

* Subtract b2

a2 − b2 = ab − b2

* Factor both sides

(a − b)(a + b) = b(a − b)

* Divide out (a − b)

a + b = b

* Observing that a = b

b + b = b

* Combine like terms on the left

2b = b

* Divide by the non-zero b

2 = 1

Q.E.D.

The fallacy is in line 5: the progression from line 4 to line 5 involves division by (a − b), which is zero since a equals b. Since division by zero is undefined, the argument is invalid.

A variation:

* Let x and y be equal, non-zero quantities

x = y

* Add x to both sides

2x = x + y

* Take 2y from both sides

2x − 2y = x − y

* Factor out a two on the left side

2(x − y) = x − y

* Divide out (x − y)

2 = 1

Q.E.D.

The fallacy here is the same as above in that by dividing by (x − y), you are dividing by zero and as such, this argument is invalid. Also by this argument:

Answer 2

The answer is no, 2 = 1 is not possible.

There is an error in your working. You start by letting x = y, but further on you divide both sides of your equation by (x - y).

This is NOT allowed !! Why ? Because, if x = y, (x - y) = 0, so you are dividing by ZERO !!

Division in only allowed when the number or expression you are dividing by is NOT ZERO.

Answer 3

Let me ask you, what is 1 ? what is 2 ?
For me 2 is just a curve. But we have defined this curve to be known as two, to denote a pair of something. Similarly, 1 too is defined by us.
For you, you can make up some maths such that 1 = 2. I can call
" # " as one and " @ " as two. It all upto me.

As for the mathematical proof of your arguement, it is baseless, as division by 0 is not defined. If you really want to prove 1 = 2, or any thing, why take so many steps.

Clearly, mention
0 = 0.
1 * 0 = 2 * 0
Cancelling out 0's,
1 = 2

This can be possible in some Maths if you can prove division of 0 is possible.

Answer 4

The final step, divide the two aspects by a-x? a = x so a-x = 0. the end results of dividing by 0 is undefined. think of roughly it. a x 0 = 0 divide by 0 and a = a million so any extensive type may well be equivalent to a minimum of one, if branch by 0 have been allowed and defined. because of fact of this branch by 0 isn't allowed.

Answer 5

You divided by zero

Answer 6

;) check out steps 4-5. you divided by zero, which screws up everything.

Answer 7

"
....
After factorising both sides, we get:
(x+y)(x-y) = y(x-y)
If we divide (x-y) from both sides: ... "

you can't divide (x-y) from both sides because x = y means x-y = 0, and you can't divide by 0

Answer 8

1 and 2 are infact the same thing observed from different precepts.

Answer 9

Your very first step is wrong. You are multiplying one side by x and one side by 2.

Answer 10

since x=y then dividing by x-y is dividing by 0... good one dude good one