The Seven Magic Theorems of Mathematics 
   -by Pawan Rama Mali

# Theorem 1.
    => 3=4.

Proof =>

Suppose a + b = c.
i. e. (4a - 3a) + (4b - 3b) = (4c - 3c)
i. e. 4a + 4b - 4c = 3a + 3b - 3c  [ After reorganising ]
i. e. 4*(a+b-c) = 3*(a+b-c)  [ Taking constants out of brackets ] 
i. e. 4 = 3
Hence the proof.

# Theorem 2.
    => All numbers are equal to zero.

Proof =>

Suppose a = b.
Let sqr  = square.
Let sqrt = square root of.
As a = b,
therefore ( a sqr 2 ) = ab
i. e. ( a sqr 2 ) - ( b sqr 2 ) = ab - ( b sqr 2 )
i. e. ( a + b ) * ( a - b ) = b*( a - b ) 
i. e. a + b = b
i. e. a = 0 ( zero )
Hence the proof.

# Theorem 3.
    => 1$(dollor) = 1c(cent)

Proof =>

And another that gives you a sense of money disappearing...

1$ = 100c
   = (10c) sqr 2
   = (0.1$) sqr 2
   = 0.01$
1$ = 1c
Hence the proof.

# Theorem 4.
      => 1 = -1.

Proof =>

We know 1 = 1.

       1   -1 
i. e. -- = --
      -1    1
           _____                 _____
     [    /  1   ]         [    / -1   ]
i.e. [   /  --   ] sqr  =  [   /  --   ] sqr
     [ \/   -1   ]         [ \/    1   ]

         ___               _____ 
     ( \/ 1  ) sqr     ( \/ -1  ) sqr

i.e. -------------  =  --------------
         ____               ____
     ( \/ -1  ) sqr     ( \/ 1   ) sqr

            ___                 ___                 ____                 ____ 
i. e. [ ( \/ 1  ) sqr ] * [ ( \/ 1  ) sqr ] = [ ( \/ -1  ) sqr ] * [ ( \/ -1  ) sqr ]
              ___                         ____  
i. e. [ [ ( \/ 1  ) sqr ] sqr ] = [ [ ( \/ -1  ) sqr ] sqr ]
        ___     ____
i. e. \/ 1  = \/ -1 
 
i. e. 1 = -1     [ Squaring both the sides ]

Hence the proof.

# Theorem 5.
     => 4=5.

Proof =>

We know  -20 = -20
i. e. 16 - 36  =  25 - 45 
i. e. ( 4 sqr 2 ) - ( 9 * 4 ) = ( 5 sqr 2 ) - ( 9 * 5 )
Now add the term (81/4) on both of the sides.
i. e. ( 4 sqr 2 )-( 9 * 4 )+( 81/4 ) = ( 5 sqr 2 )-( 9 * 5 )+( 81/4 )
i. e. ( 4 - ( 9/2 ) ) sqr = ( 5 - ( 9/2 ) ) sqr
i. e. ( 4 - ( 9/2 ) ) = ( 5 - ( 9/2 ) )
i. e. 4 = 5.
Hence the proof.

# Theorem 6.
     => A cat has nine tails.

Proof =>
No cat has eight tails. But a cat has one tail more than no cat.
Therefore a cat has nine tails.
Hence the proof.

# Theorem 7.
        => sin x = 6n.

Proof =>
To prove that sinx = 6n

                    sinx
i.e. to prove that ------ = 6
                      n

Canceling n from upper & lower sides, we get

six = 6
which is always true.
Hence the proof.

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