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**saarvin89****Member**- Registered: 2006-04-25
- Posts: 1

please proof for tat tis is true

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

I guess this is a joke?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,391

-1²=1²

(1-2)² = (2-1)²

Taking square root on both the sides,

1-2=2-1

2=4

Dividing both the sides by 2,

1=2.

But we know 1+1=2,

Therefore,

1=1+1

or

1+1=1

Character is who you are when no one is looking.

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**coolwind****Member**- Registered: 2005-10-30
- Posts: 30

ganesh wrote:

-1²=1²

(1-2)² = (2-1)²

Taking square root on both the sides,

1-2=2-1

2=4

Dividing both the sides by 2,

1=2.

But we know 1+1=2,

Therefore,

1=1+1

or

1+1=1

cool...:cool:

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**naturewild****Member**- Registered: 2005-12-04
- Posts: 30

That's... smart!

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

That's ... ganesh!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

(1-2)² = (2-1)²

Taking square root on both the sides,

1-2=2-1

Noooo...:

a^2=b^2 => |a|= |b|, not a=b.

*Last edited by krassi_holmz (2006-05-01 00:15:14)*

IPBLE: Increasing Performance By Lowering Expectations.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

ok then, how about this false proof

-1/1 = 1/-1

sqrt(-1/1) = sqrt(1/-1)

sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) or..

i/1 = 1/i

i/2 = 1/(2i)

i/2 + 3/(2i) = 1/(2i) + 3/(2i)

i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) )

(i^2)/2 = (3i)/2i = i/(2i) + (3i)/(2i)

(-1)/2 + 3/2 = 1/2 + 3/2

-1/2 = 1/2

-1 = 1

The Beginning Of All Things To End.

The End Of All Things To Come.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,391

luca-deltodesco wrote:

ok then, how about this false proof

-1/1 = 1/-1

sqrt(-1/1) = sqrt(1/-1)

sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) or..

i/1 = 1/i

There lies the mistake.

As krassi_holmz rightly pointed out in the previous post,

If

then

or

It would not be right to say a=b.

When square root is being taken on both sides of an equation, the plus or minus/minus or plus sign has an important role to play, it cannot be overlooked.

When you had taken the square roots of the LHS and the RHS in steps 2, 3, you have taken only the positive values. Remember square root on 1 is not +1 alone, it is ±1.

Character is who you are when no one is looking.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Good explamation.

IPBLE: Increasing Performance By Lowering Expectations.

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**Affirmation****Guest**

x=y

x*x = y*y

x*y = y*y | - x*x

x*y - x*x = y*y - x*x

x(y-x) = (y-x)*(y+x) | /(y-x)

x = y + x

x = x + x

x = 2x

1 = 2

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,391

Affirmation wrote:

x(y-x) = (y-x)*(y+x) | /(y-x)

The (erroneous) proof started with x=y.

Hence, x-y=0 and y-x=0.

The two sides of an equation should not be divided by zero, it may lead to absurd results!

Character is who you are when no one is looking.

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**Affirmation****Guest**

Correct Of course there will always be something wrong as 1 cannot equal 2

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,535

We had another collection of false proofs somewhere here - maybe I should collect them and make a page about it.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,562

1 will not equal 2 as long as we judge them to be different.

**igloo** **myrtilles** **fourmis**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

1 = 2 in mod 0.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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