A puzzle. Does 2=1? What gives?

Question

let x=y
then x*x=x*y (multiply both sides by y)
then x*x-y*y=x*y-y*y (subtract y*y from each side)
then (x-y)(x+y)=y(x-y) (factor)
then x+y=y (divide both sides by x-y )
then y+y=y (since x=y)
then 2y=y (add like terms)
then 2=1 (divide both sides by y)

Answer 1

Continue your proof. Bertrand Russell and the Pope are (or were) two entities. But since 2=1, Bertrand Russell and the Pope are one entity. Therefore, Bertrand Russell was the Pope.

Actually, anything goes after you divide by x-y since x-y is zero.

Answer 2

no 2=2

Answer 3

No, that's just not reasonable. You've convinced yourself that you know what you're doing, but you don't.

For example if X=Y then
(x-y) would equal zero ... so
(x-y)(x+y)=0 ... and y(x+y) only equals 0 if x=0
...
And you can't divide by 0 so x can't = zero unless you go into some psychotic mathematics with imaginary numbers ... but your equations don't show enough knowledge to be aiming for an answer with imaginary numbers or calculus.

If you are attempting to make that a series of equations that each relate to the others solution you need to clarify with non-x's/non-y's.

Lay off the absinthe and reread your homework.

Good luck with that.

Answer 4

In the second to last step, if 2y=y then y=0 and you cant divide anything by zero, so the last step (divide both sides by y) is invalid.

Answer 5

It is not possible to divide by zero, but that is exactly what you are doing in the 5th line. (If x = y, then x - y = 0). This turns the entire thing into gibberish and is a common trick in nonsense problems.

Answer 6

When you (divide both sides by x-y),

you are dividing both sides by 0,

Since x=y,

Therefore the term (x - y) = (y - y) = 0

In mathematics, division by zero is undefined.

Answer 7

I concur. Division by zero is a big no-no.

Bt if I remember correctly, you can prove 2=1 with Linear Algebra. It was a while ago, though.

Answer 8

Division by zero

Answer 9

they would have to both be zero

but that means that x-y=0, so you can't divide by it

no solution, my n00bface friend

Answer 10

certainly. 2 people engaged to each other would make one couple. 2 shoes make one pair.