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Ask iit jee aieee pet cbse icse state board experts Expert Question: Proof required
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vishy_1990 (20)

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Sir/Madam
A few months back My sir derived the derivation for prooving 1=0
But i forgot it now.
Can u please derive it for me
    
ashwin123 (255)

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I dont think there is any kind of proof like that.
 
Some people try it by assuming a=b and go on but they divide by 0(ie b-a)
which is not possible
 
My apologies to those who couldn't understand what i wrote above but i guess vishy u might understand this if ur sir has proceeded like this.
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Avinash_Bhat (655)

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I think everyone got Ashwin...
 
Let me put down a very simple example :
Initially it is given that, a and b are two positive integers such that :
             
                                                       a = b
                                                     a2 = ab
                                               a2 - b2 = ab - b2
                                       (a + b)(a - b) = b(a - b)
                                                (a + b) = b
                                                        a = 0
 
But is not 'a', a positive integer ??!! Now the hidden mistake made over here is that in the 4th step, you cancelled (a - b) on both sides which is not possible as a = b and that (a - b) = 0. These types of tricky proofs can be brought through very complex words that you may not notice the mistakes made....   
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chirag (384)

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Lets have a look at these example..:-
 
x=0
x=0x...(Since any thing multiplied by zero is zero.)
therefore,
1=0....(cancelling x both the sides)
 
Similarly, you can do this for other numbers....
 
Please rate me....
 
thanx...



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chirag (384)

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This is an another interesting example..
 
log19=x....(x is any variable..Its value depends upon your wish)
therefore,
 
1x=9
 
therefore,
since 1 raise to any power is 1, expect that it is not between 0 and 1, likewise cube roots of unity...
 
1=9..
 
Similarly, you can do this for any number..
 
The mistake here is taking base as 1, which is not permitted..
 
Please rate me...
 
Thanx...
 
 



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kusum (206)

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hi,
but then I m very sorry chirag ,since u have already assumed which is wrong at the very first statement ,u cant go on to prove something out of it .pls let me know if it has to be done this way ,otherwise it seems more unsensible to me .
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avinash.sharma (1189)

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vishy_1990  it is not possible to prove 1=0 without assuming something wrong by Mathematics. If we make a some of one page long than it's possible that we can not find a mistake. but lets me try to prove :
 
  0 = 0  it's true for all conditions
 
 0. 1 = 0. 0          it's also true for all condtions
 
Now cancel the zeroes both side as we use in algebra that
a.b=a.c    b =c
 
1=0   Hense proved.  
 
But remeber in Mind that we can not zeroes as I have done.
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