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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? smile


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

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,222

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 big_smile


Character is who you are when no one is looking.

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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 big_smile

cool...:cool:

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

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

Re: 1+1=1

That's... smart!

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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

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: 1,908

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

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


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The End Of All Things To Come.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,222

Re: 1+1=1

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

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

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
Moderator
Registered: 2005-06-28
Posts: 15,222

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!


Character is who you are when no one is looking.

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

Affirmation
Guest

Re: 1+1=1

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

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

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,555

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: 3,582

Re: 1+1=1

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


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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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