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## #1 2006-04-25 00:43:41

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

### 1+1=1

please proof for tat tis is true

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## #2 2006-04-25 01:25:40

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

### Re: 1+1=1

I guess this is a joke?

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## #3 2006-04-25 02:57:39

ganesh
Registered: 2005-06-28
Posts: 23,209

### Re: 1+1=1

-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

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #4 2006-04-30 04:29:44

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

### Re: 1+1=1

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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## #5 2006-04-30 21:35:09

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

That's... smart!

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## #6 2006-04-30 23:14:05

MathsIsFun
Registered: 2005-01-21
Posts: 7,664

### Re: 1+1=1

That's ... ganesh!

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

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## #7 2006-05-01 00:14:47

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: 1+1=1

(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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## #8 2006-05-05 05:26:30

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

### Re: 1+1=1

-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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## #9 2006-05-05 16:06:17

ganesh
Registered: 2005-06-28
Posts: 23,209

### Re: 1+1=1

luca-deltodesco wrote:

-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.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #10 2006-05-05 19:37:17

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: 1+1=1

Good explamation.

IPBLE:  Increasing Performance By Lowering Expectations.

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## #11 2006-05-05 20:28:32

Affirmation
Guest

### Re: 1+1=1

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

## #12 2006-05-05 22:13:40

ganesh
Registered: 2005-06-28
Posts: 23,209

### Re: 1+1=1

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!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #13 2006-05-06 02:40:54

Affirmation
Guest

### Re: 1+1=1

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

## #14 2006-05-06 12:08:35

MathsIsFun
Registered: 2005-01-21
Posts: 7,664

### Re: 1+1=1

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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## #15 2006-05-09 12:03:19

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: 1+1=1

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

igloo myrtilles fourmis

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## #16 2006-05-09 13:09:04

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

### Re: 1+1=1

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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