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Tuesday, October 14, 2008

2 is 1

A discussion over at Good Math, Bad Math reminded me of this - My favorite math riddle:

Proof that 2 = 1

Start with: X = Y
multiply both sides by X: X*X = X*Y
subtract Y^2 from both sides: X^2 - Y^2 = X*Y - Y^2
do some factoring: (X+Y)*(X-Y) = Y*(X-Y)
divide both sides by (X-Y): (X+Y) = Y
substitute Y for X: (Y+Y) = Y
divide by Y and simplify: 2 = 1


There you have it, a mathematical proof that two is equal to one!
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2 comments:

  1. AnonymousAugust 1, 2011 at 1:29 PM

    >Start with: X = Y
    ...
    >divide both sides by (X-Y): (X+Y) = Y

    X=Y
    =>X-Y=0

    So you are actually trying to divide by zero which is not permitted in this context (an undefined operation).

    See also:
    http://en.wikipedia.org/wiki/Division_by_zero

    ReplyDelete
  2. Dan EastwoodAugust 1, 2011 at 7:15 PM

    Yes, Anon. I am dividing by zero, it's funnier that way.

    See also:
    http://en.wikipedia.org/wiki/Humour

    ReplyDelete