Ramanujam's proof!!.... can u find any flaws??

jkbytes · Posted: Tue May 31, 2005 3:37 pm

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

9-15 = 4-10

adding 25/4 to both sides:

9-15+25/4 = 4-10+25/4

Changing the order

9+25/4-15 = 4+25/4-10

(this is just like a square + b square - two a b = (a-b)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:

(3-5/2)(3-5/2) = (2-5/2)(2-5/2)

Taking positive square root on both sides:

3 - 5/2 = 2 - 5/2

3 = 2 ????????

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

Hi,

The following is not true always :

if (a-b)^2 = (c-b)^2
then (a-b) = (c-b)

The right expression will be :

if (a-b)^2 = (c-b)^2
then (a-b) = +/-(c-b)

If you take the + sign then only 2 = 3 otherwise not.

Let us not make 2=3.

jkbytes · Posted: Wed Jun 01, 2005 5:30 pm

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 -

(3-5/2)(3-5/2) = (2-5/2)(2-5/2)

This reduces to (a -c ) square = (b -c) square ....... (1)

The falacy is - if you accept ( 3 - 2 ) equals a non-zero value then this Ramanujam statement does not stand as follows -

(a-c) square - (b-c) square = 0 [ From (1) ]

or ( (a-c) + (b-c) ) * ( (a-c) - (b-c) ) = 0

or ( a-2c + b) * (a -b) = 0 ......(2)

Now the falacy comes -

For this equation to be satisfied
either (a-2c+b) has to be equal to zero
or (a-b) 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) * (3-2) = 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 ( 3-2 ) 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

jkbytes · Posted: Thu Jun 02, 2005 9:35 am

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.

David P · Posted: Thu Jun 02, 2005 10:50 am

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.

jkbytes · Posted: Thu Jun 02, 2005 11:47 am

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.