I Love Math - How can 1 == 2 ?

[Raging_Geek]

How can 1 == 2 ? - Proof:

assume

x == y

then

x^2 == xy (multiply both sides by x)

x^2 - y^2 == xy - y^2 (subtract y^2 from both sides)

(x + y)(x - y) == y (x - y) ( factor both sides )

now we can cancel the (x-y) because we have it on both sides

x + y == y

y + y == y (since x == y above we can substitute x for y)

2y == 1y

2 == 1 !!!!!!!!

Q.E.D.

 

[chuck1561]

great......now I'm going to go to bed with a fuckin brain cramp!

HFS

I know whatch'ya mean HiFi

oops sorry ..that's a brain fart well ya take what you can get at this time of the morning

 

[hitrack]

COOL!!

I also like the one where Lou Costello is trying to convince this other guy that 7x13=28

 

[ironchef]

given that you the formula must satisfy x=y and y=y+x
x and y must both equal zero

 

[Raging_Geek]

given that you the formula must satisfy x=y and y=y+x
x and y must both equal zero

Nope! But your close....

y == y+ x

is derived from x == y

sorry for the brain farts - but saw HardAtWork's "Math scare's me" got to thinking about this post and could not resist...

hehehe

 

[wolverine]

x^2 - y^2 == xy - y^2 (subtract y^2 from both sides)

(x + y)(x - y) == y (x - y) ( factor both sides )

It's been ages since I took calculus, so I don't understand how you derived this "factor both sides" thing.

 

[Raging_Geek]

(x + y)(x - y) == y (x - y) ( factor both sides )

x^2 - y^2

is a difference of squares and factors to

(x - y)(x + y)

try to multiply it back and you get

x*x + x*y - x*y - y*y

x*x - y*y

x^2 - y^2

thats the right side, now the left side...

xy - y^2 == x*y - y*y == y*(x-y) == y(x - y)

factoring out the y on the left side

hope that explains the factoring

but where is the problem or does 1 really equal 2???

hehehe

 

[chuck1561]

Re: (x + y)(x - y) == y (x - y) ( factor both sides )

x^2 - y^2

is a difference of squares and factors to

(x - y)(x + y)

try to multiply it back and you get

x*x + x*y - x*y - y*y

x*x - y*y

x^2 - y^2

thats the right side, now the left side...

xy - y^2 == x*y - y*y == y*(x-y) == y(x - y)

factoring out the y on the left side

hope that explains the factoring

but where is the problem or does 1 really equal 2???

hehehe

OK ...NOWWWW You've DONE IT

ok think nice thoughts..niiiiiice thoughts

Football..lol

TOUCH and FEEL football..

 

[Avery]

How can 1 == 2 ? - Proof:

assume

x == y

then

x^2 == xy (multiply both sides by x)

x^2 - y^2 == xy - y^2 (subtract y^2 from both sides)

(x + y)(x - y) == y (x - y) ( factor both sides )

now we can cancel the (x-y) because we have it on both sides

x + y == y

y + y == y (since x == y above we can substitute x for y)

2y == 1y ***

2 == 1 !!!!!!!!

Q.E.D.

***It breaks down here because the only value of y that satisfies that equation is zero. Division by zero is impossible; anytime a real number is divided by zero, the answer is infinity.

Therefore, the final line is not 2 = 1; it's infinity = infinity.

 

[bobsled]

X and Y

Raging Geek...

I should dig up some of my Absract Algerba...

Your Proof rings true, but only if X and Y are zero.

Actually, I think it was the Mayans that came up with the concept of a Zero. I don't really know. My last girlfriend used to call me that. God, I miss her.

I noticed that there is no division in your Proof. Then your Proof would explode.

Can you propose a similar Proof using division, assuming X=Y....?

Challenge....

bobsled.

PS
I'm having fun with this.....

 

[LonelyGhost]

I thought it was the Indians who invented zero.

 

[Raging_Geek]

Re: Re: I Love Math - How can 1 == 2 ?

***It breaks down here because the only value of y that satisfies that equation is zero. Division by zero is impossible; anytime a real number is divided by zero, the answer is infinity.

Therefore, the final line is not 2 = 1; it's infinity = infinity.

Beautiful!!!!

Thats it!!!

Dividing by a disguised zero is exactly the trick here!

(x - y) == 0 when x == y

and when we cancel the (x - y) by dividing both sides by (x - y)
its infact dividing both sides by zero

0 == 0

2* 0 == 1* 0

Divide by zero

2*0/0 == 1*0/0

2 == 1

But we cannot divide by zero - hence the proof is false.

Well done Avery!