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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
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,423
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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
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
-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
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: 7,713
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
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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#9 2006-05-05 16:06:17
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
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
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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
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
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- 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
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: 1+1=1
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 appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
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
- Administrator
- Registered: 2005-01-21
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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
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- Registered: 2005-08-29
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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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