Problem of the Day
A new programming or logic puzzle every Mon-Fri

2=1

Does 2 = 1 or is there an error with this proof?

             a = b
            aa = ab
       aa - bb = ab - bb
(a + b)(a - b) = b(a - b)
         a + b = b
         a + a = a
            2a = a
             2 = 1

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Permalink: http://problemotd.com/problem/2-equals-1/

Comments:

  • brendon - 11 years, 2 months ago

    the 4th step. if a = b then (a - b) = 0 and since both sides divide (a - b) .. or 0.. there is an error

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  • Johnathan - 11 years, 2 months ago

    Well looking at the last two steps. 2a = a a has to be = 1 if b = a b = 1

    so fill in 1 for both a and b. 1 = 1 OK 1*1 = 1*1 OK (1*1) - (1*1) = (1*1) - (1*1) OK (1 + 1)(1 - 1) = 1(1 - 1) OK 1 + 1 = 1 Error 1 + 1 = 1 Error 2*1 = 1 Error 2 = 1

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  • bzxbot - 11 years, 2 months ago

    In the fifth step, both sides are divided by (a - b). Since a = b, (a - b) is equal to 0, resulting in a 0/0 division. 0/0 is indetermined, therefore the fifth step is not valid.

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