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Ahouxs.130 net.math utzoo!decvax!harpo!ihnss!houxi!houxv!houxs!hansen Tue May 4 12:47:42 1982 An oldie but goodie Here's an old paradox I remember from my school days. Find which steps in this proof are wrong, and what rules they violate.

Enjoy, Tony Hansen houxs!hansen ***************************************************************************** Prove: -1 is equal to 1. *****************************************************************************

---- ---- 1. v -1 = v -1 identity axiom, sqrt(a)=sqrt(a)

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2. ------ / -1 ---- / --- = v -1 property of 1 v 1

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------ ------ 3. / -1 / 1 / --- = / --- property of negative numbers v 1 v -1

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---- ---- v -1 v 1

4. ________ = ________ sqrt(a/b) = sqrt(a)/sqrt(b)

---- ---- v 1 v -1

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---- ---- ---- ---- 5. v -1 * v -1 = v 1 * v 1 cross multiply

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6. -1 = 1 Q.E.D. (?!? Surprise ?!?)

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