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jkbytes
Active User
Joined: 19 Feb 2005 Posts: 141 Location: South Africa




Hi,
Can U Prove 3=2??
This seems to be an anomaly or whatever u call in mathematics.
It seems, Ramanujam found it but never disclosed it during his life time and that it has been found from his dairy.
See this illustration:
6 = 6
915 = 410
adding 25/4 to both sides:
915+25/4 = 410+25/4
Changing the order
9+25/415 = 4+25/410
(this is just like a square + b square  two a b = (ab)square.)
Here a = 3, b=5/2 for L.H.S and a =2, b=5/2 for R.H.S.
So it can be expressed as follows:
(35/2)(35/2) = (25/2)(25/2)
Taking positive square root on both sides:
3  5/2 = 2  5/2
3 = 2 ???????? 

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arunoday
New User
Joined: 17 May 2005 Posts: 18 Location: Bangalore




Hi,
The following is not true always :
if (ab)^2 = (cb)^2
then (ab) = (cb)
The right expression will be :
if (ab)^2 = (cb)^2
then (ab) = +/(cb)
If you take the + sign then only 2 = 3 otherwise not.
Let us not make 2=3. 

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jkbytes
Active User
Joined: 19 Feb 2005 Posts: 141 Location: South Africa




arunoday wrote: 
Let us not make 2=3. 
I wonder what does that mean.......


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arunoday
New User
Joined: 17 May 2005 Posts: 18 Location: Bangalore




hi,
This is a simple joke  " Let us not make 2=3. "
On the serious part 
Let us take a = 3, b= 2, c = 5/2
The expression with square ( in the whole sqaure form ) is 
(35/2)(35/2) = (25/2)(25/2)
This reduces to (a c ) square = (b c) square ....... (1)
The falacy is  if you accept ( 3  2 ) equals a nonzero value then this Ramanujam statement does not stand as follows 
(ac) square  (bc) square = 0 [ From (1) ]
or ( (ac) + (bc) ) * ( (ac)  (bc) ) = 0
or ( a2c + b) * (a b) = 0 ......(2)
Now the falacy comes 
For this equation to be satisfied
either (a2c+b) has to be equal to zero
or (ab) has to be equal to zero
or both the factors have to be equal to zero
Here if we put value of a,b,c we get 
(3 2*5/2 + 2) * (32) = 0 [ From 2 ]
The first factor is already becoming equal to zero so the whole expression is becoming zero and there is no need that second factor to be zero.
So ( 32 ) not equal to zero So 3 not equal to 2
If we take ( 3  2 ) = 0 then there will be no difference between the numbers 3 and 2. Because as a result of subtraction zero is produced only when we subtract the number from itself.
SO 3 CAN NEVER BE EQUAL TO 2. IT IS ACTUALLY A FALACY AND NOT A FACT.
Thanks 

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jkbytes
Active User
Joined: 19 Feb 2005 Posts: 141 Location: South Africa




woooooooooooo,
Toooooo much of mathematics is not good for my health.....
But let us consider.
Let a=0; b=0 ; therefore a+b =0;
Which brings that 2a=3a=a=0;
so
a+b=3a;
substitute a=2a
2a+0 = 3a;
2a=3a
cancellling a on both sides
2=3.
Iam not sure about this but i guess some theorem stands behind this strongly. 

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David P
Active User
Joined: 11 Apr 2005 Posts: 106 Location: Cincinnati Ohio




Hi jkbytes,
Its getting really intersting...but I think one point you missed here ...
if
2a=3a
and a=0; you can not cancel a from both the sides. You can cancel only nonzero values from both side of any equation.
other wise not only you can prove 2=3 but you can prove all the numbers
equal to each other.
I hope you got what I am saying. Though I am really enjoying these calculations.
regards,
David. 

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jkbytes
Active User
Joined: 19 Feb 2005 Posts: 141 Location: South Africa




Hi david,
As you have mentioned this is getting interesting eachtime.
Even though i'm not able to prove 2=3,
i was able to prove that two part of something is equal to three part of the same thing. provided the thing is null.
converse: vice versa. 

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