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Prove That 1 = 2

If a = b and b > 0 and a > 0, then 1 = 2
a>0 and b>0
a = b
ab = b2
ab - a2 = b2 - a2
a(b-a) = (b+a)(b-a)
a = (b+a)
a = a + a (substituting a for b)
a = 2a
a/a = 2a/a
1 = 2




     a = x            [true for some a's and x's]
   a+a = a+x          [add a to both sides]
    2a = a+x          [a+a = 2a]
 2a-2x = a+x-2x       [subtract 2x from both sides]
2(a-x) = a+x-2x       [2a-2x = 2(a-x)]
2(a-x) = a-x          [x-2x = -x]
     2 = 1            [divide both sides by a-x]



             a = b
            a2 = ab
       a2 - b2 = ab - b2
(a + b)(a - b) = b(a - b)
         a + b = b
            2b = b
             2 = 1


           (x + 1)2 = x2 + 2x + 1
(x + 1)2 - (2x + 1) = x2
(x + 1)2 - (2x + 1) - x(2x + 1) = x2 - x(2x + 1)
(x + 1)2 - (x + 1)(2x + 1) + (1/4)(2x + 1)2 = x2 - x(2x + 1) + (1/4)(2x + 1)2
[(x + 1) - (1/2)(2x + 1)]2 = [x - (1/2)(2x + 1)]2
(x + 1) - (1/2)(2x + 1) = x - (1/2)(2x + 1)
x + 1 = x
1 = 0
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