2 = 1

[Graeme]

I'm sick and tired of having people agree with me so often, so I'm now going to make a statement that hopefully not too many people will agree with me....

 

2 = 1

 

Controversial, I know, but I've seen the proof. The following will get a bit scary for those mathematically challenged, but here goes...

 

Let x = y

 

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

 

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

 

=> (x - y)(x + y) = y(x - y) (factorise)

 

=> x + y = y (divide both sides by (x - y)

 

=> x + x = x (because we started with x = y)

 

=> 2x = x (simplify)

 

=> 2 = 1 (divide both sides by x)

 

Q.E.D.

[BeaStKid]

[steph]

I'm sick and tired of having people agree with me so often, so I'm now going to make a statement that hopefully not too many people will agree with me....

 

We can't help it, Graeme, when you are a fountain of amazing insight! After reading your posts, I often think that you must be a wonderful dad! *sigh* you have any brothers?

 

...

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

=> x + y = y (divide both sides by (x - y))

...

 

:nuke: Danger! Danger! :nuke:

[rknapp]

This of course all hinges on x equaling y. The second any number is associated with these variables your calculations become null and void, particularly at the second step (subtracting y^2 from both sides). BUT your maths remind of another proof that is more relavant to our male-driven society.

 

What about this:

 

 

We know that women like two things, your time and your money, therefore...

 

women = time x money

 

 

 

Now time equals money, so

 

women = money x money

 

 

 

Money is the root of all evil, so

 

money = square root of evil

 

 

 

By squaring both sides of the equation,

 

money squared = evil

 

 

 

Now go back to the equation

 

women = money x money

 

 

 

See where I'm headed?

 

women = money squared = evil

 

 

 

A problem with this "proof" occurred to me immediately: Since evil is negative, the square root of evil must be imaginary, which would mean that money is imaginary, and therefore, by definition, so is time.

 

Then I realized that, in my life at least, that's pretty much true.

[YaP]

This of course all hinges on x equaling y. The second any number is associated with these variables your calculations become null and void, particularly at the second step (subtracting y^2 from both sides). BUT your maths remind of another proof that is more relavant to our male-driven society.

 

What about this:

 

 

We know that women like two things, your time and your money, therefore...

 

women = time x money

 

 

 

Now time equals money, so

 

women = money x money

 

 

 

Money is the root of all evil, so

 

money = square root of evil

 

 

 

By squaring both sides of the equation,

 

money squared = evil

 

 

 

Now go back to the equation

 

women = money x money

 

 

 

See where I'm headed?

 

women = money squared = evil

 

 

 

A problem with this "proof" occurred to me immediately: Since evil is negative, the square root of evil must be imaginary, which would mean that money is imaginary, and therefore, by definition, so is time.

 

Then I realized that, in my life at least, that's pretty much true.

 

lol, very nice

[Menzoberranzen]

If only division by zero were possible...

[Ieshwar]

Menzo, it is possible! In the world where infinity exists!

 

Nice one, graeme but I already knew it. The Robbie one too except for the imaginary part... interesting!

 

Ieshwar

[Menzoberranzen]

Menzo, it is possible! In the world where infinity exists!

 

Nice one, graeme but I already knew it. The Robbie one too except for the imaginary part... interesting!

 

Ieshwar

 

But x/0 doesn't equal infinity. That's just the limit. x/0 is undefined.

[Tiger]

I'm sick and tired of having people agree with me so often, so I'm now going to make a statement that hopefully not too many people will agree with me....

 

2 = 1

 

Controversial, I know, but I've seen the proof. The following will get a bit scary for those mathematically challenged, but here goes...

 

Let x = y

 

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

 

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

 

=> (x - y)(x + y) = y(x - y) (factorise)

 

=> x + y = y (divide both sides by (x - y)

 

=> x + x = x (because we started with x = y)

 

=> 2x = x (simplify)

 

=> 2 = 1 (divide both sides by x)

 

Q.E.D.

I respectfully disagree.

[rknapp]

But x/0 doesn't equal infinity. That's just the limit. x/0 is undefined.

That is correct, further evidence that Graeme's calculations are flawed if any numbers are involved to represent the variables.

[Razor]

......................................................................

 

~brain asplodes~ I hate math, lol. I blame the way it's taught in the US... they need more Socratic method, less textbook examples. If I'd had a personal tutor going "Well, you know how to do blahblahblah. Now, what if we wanted to find blahblahblah? Can you think of any good way to do that?", then I think I would have found the concepts easier to grasp quickly and fully, and I think I'd have ended up really enjoying math. I'm not bad at it, it just bores me into oblivion and I never had a good math teacher till 10th grade.

 

And I've heard the women are evil proof before... I used to have a .gif of it.

[colinian]

We cannot let this go on without a rejoinder. Let's do that by substituting right from the get-go. I'll substutute 2 for x and 2 for y as we step through Graeme's lovely formulas. Let's see if this actually works:

 

I'm sick and tired of having people agree with me so often, so I'm now going to make a statement that hopefully not too many people will agree with me....

 

2 = 1

 

Controversial, I know, but I've seen the proof. The following will get a bit scary for those mathematically challenged, but here goes...

 

Let x = y Therefore 2 = 2

 

=> x^2 = xy (multiply both sides by x) Therefore 2^2 = 2*2 {{or, 4 = 4; so far, so good}}

 

=> x^2 - y^2 = xy - y^2 (subtract y squared from both sides) Therefore 2^2 - 2^2 = 2*2 - 2^2 {{or, 4 - 4 = 4 - 4, thus 0 = 0; we're still OK}}

 

=> (x - y)(x + y) = y(x - y) (factorise) Therefore (2-2)*(2+2) = 2*(2-2) {{or, 0 * 4 = 2 * 0, thus 0 = 0; yes sir, zero still does equal zero when we factorise}}

 

=> x + y = y (divide both sides by (x - y) Therefore... hey! Wait just a darn minute! If we "divide both sides by (x - y)" as Graeme asks us to do, he's asking us to "divide both sides by (2 - 2)" but (2 - 2) = 0. Up here in the Northern Hemisphere you just cannot divide something by zero. It creates an imginary number. Dang! That's too bad. Makes his interesting algebraic exercise null and void. At least up here in the Northern Hemisphere. Maybe things are different down there in Oz on the bottom side of the planet. But somehow I don't think so!

 

=> x + x = x (because we started with x = y) Therefore this step FAILED!

 

=> 2x = x (simplify) and so did this step

 

=> 2 = 1 (divide both sides by x) and this result will never happen in the Real World

 

Q.E.D. NOT PROVED!

 

Your wish is fulfilled, Graeme. We don't agree with you. BTW, don't let your boys see this little parlor trick; their impressionable minds might be subverted!

 

Oh, and don't try starting out with 2 for x and 1 for y. That puts you on the slippery slope where 4 = 2 and 3 = 1, and... and... Hey, Graeme, here's a dollar bill (AU$), I'd like three of 'em back, please, since you claim they are equivalent. Thanks! Oh, and here are three dollar bills, I'd like nine of 'em back, please. Thank you! OH! Here are nine dollar bills, now I want 27 of 'em back. Thanks so much. Now I have 27...

 

 

Colin

[Graeme]

Is now an appropriate time to mention that I got the above from an encyclopedia that I read as a kid?

 

Yes, the problem is the division by zero. There is an unwritten (usually) assumption in any algebra that if you divide by something, that it is not zero. The result of dividing by zero is undefined, not infinity (as some people have said). You can see this by considering the following equation:

 

y = x^2 / x

 

The value at x = 0 is undefined, BUT if you take the limit as x approaches zero, you can see that the result will be zero NOT infinity. You can easily plot this and you get a simple straight line, but with a discontinuity at x = 0.

 

 

 

Okay, the next thing for people to disagree with me on (at least I hope so).

 

Australia is on the top half of the world.

 

This is obvious when you consider the fact that the Earth is reasonably stable. As any one who has played with a non-homogeneous sphere will know, the object is only really stable when the majority of the mass is in the lower half of the sphere.

 

Since most of the land mass in the world is in the Northern Hemisphere and the majority of the human population (and biological mass) is in the Northern Hemisphere, it follows that for the Earth to be stable, that Northern Hemisphere must be the bottom half of the world.

 

It's just us people living in the Southern Hemisphere are too polite (normally) to point out the obvious error in the vast majority of maps that are produced that have North at the top.

[BeaStKid]

Okay, the next thing for people to disagree with me on (at least I hope so).

 

Australia is on the top half of the world.

 

This is obvious when you consider the fact that the Earth is reasonably stable. As any one who has played with a non-homogeneous sphere will know, the object is only really stable when the majority of the mass is in the lower half of the sphere.

 

Since most of the land mass in the world is in the Northern Hemisphere and the majority of the human population (and biological mass) is in the Northern Hemisphere, it follows that for the Earth to be stable, that Northern Hemisphere must be the bottom half of the world.

 

It's just us people living in the Southern Hemisphere are too polite (normally) to point out the obvious error in the vast majority of maps that are produced that have North at the top.

LOL!!

[FrenchCanadian]

Okay, the next thing for people to disagree with me on (at least I hope so).

 

Australia is on the top half of the world.

 

This is obvious when you consider the fact that the Earth is reasonably stable. As any one who has played with a non-homogeneous sphere will know, the object is only really stable when the majority of the mass is in the lower half of the sphere.

 

Since most of the land mass in the world is in the Northern Hemisphere and the majority of the human population (and biological mass) is in the Northern Hemisphere, it follows that for the Earth to be stable, that Northern Hemisphere must be the bottom half of the world.

 

It's just us people living in the Southern Hemisphere are too polite (normally) to point out the obvious error in the vast majority of maps that are produced that have North at the top.

 

LOL, I respectfully disagree with you,, maybe you had just a little to much blood going down in your head,,

[YaP]

Australia is on the top half of the world.

 

This is obvious when you consider the fact that the Earth is reasonably stable. As any one who has played with a non-homogeneous sphere will know, the object is only really stable when the majority of the mass is in the lower half of the sphere.

 

Since most of the land mass in the world is in the Northern Hemisphere and the majority of the human population (and biological mass) is in the Northern Hemisphere, it follows that for the Earth to be stable, that Northern Hemisphere must be the bottom half of the world.

 

It's just us people living in the Southern Hemisphere are too polite (normally) to point out the obvious error in the vast majority of maps that are produced that have North at the top.

 

Well, everything is relative.. i have seen maps of the world where the southern pole was on top... and therefore Australia was on the top half. Just depends on your POV. Looking at it from a more universal point of view... i can not think of any way to "prove" that north (or south) pole have to be "up"... so for me, this statement is as true as the opposite (lol, maybe its because i live in the city where Albert Einstein was born.. but i LOVE relativity )

[S.L. Lewis]

I'm sick and tired of having people agree with me so often, so I'm now going to make a statement that hopefully not too many people will agree with me....

 

2 = 1

 

Controversial, I know, but I've seen the proof. The following will get a bit scary for those mathematically challenged, but here goes...

 

Let x = y

 

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

 

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

 

=> (x - y)(x + y) = y(x - y) (factorise)

 

=> x + y = y (divide both sides by (x - y)

 

=> x + x = x (because we started with x = y)

 

=> 2x = x (simplify)

 

=> 2 = 1 (divide both sides by x)

 

Q.E.D.

 

*twitchtwitch* I remember this and I remember that I hated it something fierce. Why must you dreg up horrible memories of math class? *cries*

Anyways...interesting post. You made me think and right now...it is much to early to be thinking.

[Aeroplane]

Australia is on the top half of the world.

 

This is obvious when you consider the fact that the Earth is reasonably stable. As any one who has played with a non-homogeneous sphere will know, the object is only really stable when the majority of the mass is in the lower half of the sphere.

 

Since most of the land mass in the world is in the Northern Hemisphere and the majority of the human population (and biological mass) is in the Northern Hemisphere, it follows that for the Earth to be stable, that Northern Hemisphere must be the bottom half of the world.

 

 

This would be fine, and there would be no fault in it if there wasnt a key omission. The non-homogenous sphere is only stable when the majority of the mass is in the lower half of the sphere *because gravity is acting to a greater extent on the greater mass*. .

 

Gravity acts at a strength inversely proportional to the distance between two objects, so while there is still gravity in space (the environment the earth is sitting in) we can say with reasonable accuracy that the only gravity acting on us in space is the attraction to the sun which is keeping us in a stable orbit. The planet is spinning, so no part of the earth is always facing the sun and experiencing the greatest gravity and so no part of the earth must be significantly heavier than the other.

 

Because of the direction the planet spins, perhaps either the eastern or the western hemisphere will eventually turn out to be heavier than the other, but not the northern or southern ;p.

[Benji]

This would be fine, and there would be no fault in it if there wasnt a key omission. The non-homogenous sphere is only stable when the majority of the mass is in the lower half of the sphere *because gravity is acting to a greater extent on the greater mass*. .

 

Gravity acts at a strength inversely proportional to the distance between two objects, so while there is still gravity in space (the environment the earth is sitting in) we can say with reasonable accuracy that the only gravity acting on us in space is the attraction to the sun which is keeping us in a stable orbit. The planet is spinning, so no part of the earth is always facing the sun and experiencing the greatest gravity and so no part of the earth must be significantly heavier than the other.

 

Because of the direction the planet spins, perhaps either the eastern or the western hemisphere will eventually turn out to be heavier than the other, but not the northern or southern ;p.

 

 

.......Well that explantion just plains sucks, and does not answer the question of why our ass's sag.

[Graeme]

LOL, I respectfully disagree with you,, maybe you had just a little to much blood going down in your head,,

You are quite free to disagree with me (the entire purpose of this thread is for people to disagree with me ) but can you at least provide some reasons? I've given my reasons why Australia is on the top half of the world....

 

Well, everything is relative.. i have seen maps of the world where the southern pole was on top... and therefore Australia was on the top half. Just depends on your POV. Looking at it from a more universal point of view... i can not think of any way to "prove" that north (or south) pole have to be "up"... so for me, this statement is as true as the opposite (lol, maybe its because i live in the city where Albert Einstein was born.. but i LOVE relativity )

Alas, those maps are very rare. This is clearly discriminatory and we should start a campaign to regain equality, as a minimum. Where do you think we should start? My suggestion would be to require that half of all text books in USA schools have South at the top of any maps....

 

This would be fine, and there would be no fault in it if there wasnt a key omission. The non-homogenous sphere is only stable when the majority of the mass is in the lower half of the sphere *because gravity is acting to a greater extent on the greater mass*. .

 

Gravity acts at a strength inversely proportional to the distance between two objects, so while there is still gravity in space (the environment the earth is sitting in) we can say with reasonable accuracy that the only gravity acting on us in space is the attraction to the sun which is keeping us in a stable orbit. The planet is spinning, so no part of the earth is always facing the sun and experiencing the greatest gravity and so no part of the earth must be significantly heavier than the other.

 

Because of the direction the planet spins, perhaps either the eastern or the western hemisphere will eventually turn out to be heavier than the other, but not the northern or southern ;p.

Damn! I was hoping no one would point that out... :wacko:

[Bondwriter]

Australia is on the top half of the world.

I didn't even read any of the arguments. My grandma used to say: "Don't argue with people who walk upside down." I love my grandma.

[YaP]

Alas, those maps are very rare. This is clearly discriminatory and we should start a campaign to regain equality, as a minimum. Where do you think we should start? My suggestion would be to require that half of all text books in USA schools have South at the top of any maps....

 

I have one of those hanging on my wall (postcard size) .

I would say ALL the text books of the planet (!) should - for the next 100 years - have South at the top of any maps, just to balance things out, because we had for such a long time the North on top of all maps.. and after that time we should have every second map showing "South" on top, even within one textbook. It helps to understand relativity

The sad thing is that some people wouldnt even notice the difference

[clumber]

Ah, but actual north or Magnetic North? Because then you'd be causing no end of trouble...