Math Logic question

[jfulcer]

How can I prove 2 = 1? What is wrong here:

X = Y

X<SUP>2</SUP> = XY

X<SUP>2</SUP> - Y<SUP>2</SUP> = XY - Y<SUP>2</SUP>

(X - Y)(X + Y) = Y(X - Y)

X + Y = Y

2X = X

2 = 1

HUH?

 

[RoqueC]

2=1 is an untrue statement, no? It'd just be ZERO.

 

[honeywolf7]

All I can tell you is that I think x=0 and 2 zeros is the same as one zero. The proving part is up to you

 

[SPAGo 98]

Originally posted by jfulcer
(X - Y)(X + Y) = Y(X - Y)

X + Y = Y

in this step, you're dividing by zero since X = Y, therefore X - Y = 0. you can't divide by zero.

 

[Steve H.]

Spago -- there's no division in any of the statements listed, only multiplication, thus X and Y can both be 0

 

[Toby'sFriend]

I'm going to agree with Spago.

To get to X + Y = Y you would need to divide both sides of the equation by (X - Y). Since X = Y then X - Y = 0 and you can't divide by 0.

 

[D Dragon]

Actually Spago is close but not correct.

In jfulcer's next to last line:

2X=X

the next step is:

2X - X = 0

then

X = 0

Therefore

X = Y = 0

 

[Toby'sFriend]

http://mathworld.wolfram.com/Fallacy.html

This site gives an explanation.

 

[nabrkeshikki]

Your math is wrong...

(X - Y)(X + Y) = Y(X - Y)
should be
(X - Y)(X + Y) = 2Y(X - Y)
x+y = 2y
2y =2y

I don't think you can prove what isn't provable...
sorry for my first post being nerdy - I'm a EE with a minor in math, NERD!!!
OOPS!! misunderstood your question... now I'm a EE with a minor in math & a PHD in DUHHHH!!!

 

[jfulcer]

the logic is wrong because you cannot divide by zero in this line:

(X - Y)(X + Y) = Y(X - Y)

to get to the next statement, you have to divide both sides by (X - Y), which if X = Y is division by zero and you cannot do it.

Good brain, Spago!

 

[KathiWithAnI]

ok nabrkeshikki said that this step is wrong
X2 - Y2 = XY - Y2

(X - Y)(X + Y) = Y(X - Y)

but it isn't wrong it would not be (X - Y)(X + Y) = 2Y(X - Y)
as the OP only factored out one Y so that step is correct......
and Spago is right you would be dividing by 0 here
(X - Y)(X + Y) = Y(X - Y)

X + Y = Y because both sides were divided by (x-y) and since x=y, then that would be dividing by 0.
and you don't HAVE to say 2X=X

the next step is:

2X - X = 0

because you could have divided both sides by X ( not the normal way to solve for x, but doesn't break any rules) I think Spago's dividng by 0 statement is the real answer WHY this is wrong

Ok, now that I have written all of this, I bothered to go check the site someone listed and the "no division by 0" is the correct answer!!
Go spago, go spago and hey, I agreed... good to know I knew it since I teach algebra LOL
Kathi

 

[trayletha]

Ok - I read the whole thread and now have a headache.

 

[Wagamama]

trayletha, i feel the same way!!!!!! you want some aspirin? or maybe better, how about a corona?

 

[trayletha]

Oh yeah - ice cold with lime please

 

[KathiWithAnI]

ok and now I see that while I was posted all of the above, jfulcer posted the answer so just ignore me... as I wander away in total silence LOL

oh yeah and Toby was right too
hushing up now..........