UNsound logic

there are proofs. and there are those that
pose as proofs :p
try to figure out what's wrong with these :)


Theorem : 3=4
Proof:
Suppose:
 a    +    b    =    c
This can also be written as:
 4a - 3a + 4b - 3b = 4c - 3c
After reorganising:
 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

Theorem : All numbers are equal to zero.
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
a + b = b
a = 0

Theorem: 1$(dollar) = 1c(cent).
Proof:
And another that gives you a sense of
money disappearing...
1$ = 100c
= (10c)^2
= (0.1$)^2
= 0.01$
= 1c

Theorem: 1 = -1 .
Proof:
1/-1  =   -1/1
sqrt[ 1/-1 ]  = sqrt[ -1/1 ]
sqrt[1]*sqrt[1] = sqrt[-1]*sqrt[-1]
ie 1 = -1

    Theorem: 4 = 5
  Proof:
  16 - 36 = 25 - 45
  4^2 - 9*4 = 5^2 - 9*5
  4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4
  (4 - 9/2)^2 = (5 - 9/2)^2
  4 - 9/2 = 5 - 9/2
  4 = 5