Amazing Proofs

Three is equal to four 

Theorem: 3=4

Proof:

Suppose: a + b = c

This can also be written as:

                 4a - 3a + 4b - 3b = 4c - 3c

After reorganizing:

                 4a + 4b - 4c = 3a + 3b - 3c

Take the constants out of the brackets:

                 4 * (a+b-c) = 3 * (a+b-c)

Remove the same term left and right:

                 4 = 3 

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Dollars equal ten cents 

Theorem: 1$ = 10 cent 

Proof: 

We know that $1 = 100 cents
 Divide both sides by 100
 $ 1/100 = 100/100 cents
 => $ 1/100 = 1 cent
 Take square root both side
 => squr($1/100) = squr (1 cent)
 => $ 1/10 = 1 cent 
 Multiply both side by 10
 => $1 = 10 cent
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All numbers are equal 

Theorem: All numbers are equal.

Proof:

Choose arbitrary a and b, and let t = a + b. Then

 a + b = t

 (a + b)(a - b) = t(a - b)

 a² - b² = ta - tb

 a² - ta = b² - tb 

 a² - ta + (t²)/4 = b² - tb + (t²)/4

 (a - t/2)² = (b - t/2)²

 a - t/2 = b - t/2

 a = b

So all numbers are the same, and math is pointless.
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One equal to one half 

Theorem: 1 = 1/2

Proof:

We can re-write the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9)+... 
as 1/2((1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9) + ... ).

All terms after 1/1 cancel, so that the sum is 1/2.

We can also re-write the series as (1/1 - 2/3) + (2/3 - 3/5) + (3/5 - 4/7)+ (4/7 - 5/9) + ...

All terms after 1/1 cancel, so that the sum is 1.

Thus 1/2 = 1.
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Numbers equal zero 

Theorem : All numbers are equal to zero.

Proof:

Suppose: a=b. 

Then

  a = b
  a² = ab
  a² - b² = ab - b²
  (a + b)(a - b) = b(a - b)
  a + b = b
  a = 0
   Further more if a + b = b,and a = b,                          then b + b = b, and 2b = b,
   which mean that 2 = 1.
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Dollars equal cents

Theorem: 1$ = 1c.Proof:

Let, $ means dollars and c means cents.
 1$ = 100c
  = (10c)²
  = (0.1$)²
  = 0.01$
  = 1c 
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Four is equal to five

Theorem: 4 = 5 

Proof: 

  -20 = -20
  16 - 36 = 25 - 45

  4² - 9*4 = 5² - 9*5

  4² - 9*4 + 81/4 = 5² - 9*5 + 81/4
  (4 - 9/2)² = (5 - 9/2)²
  4 - 9/2 = 5 - 9/2
  4 = 5
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Girls are Evil

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