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) ***************************************************************************** 2. ------ / -1 ---- / --- = v -1 property of 1 v 1 ***************************************************************************** ------ ------ 3. / -1 / 1 / --- = / --- property of negative numbers v 1 v -1 ***************************************************************************** ---- ---- v -1 v 1 4. ________ = ________ sqrt(a/b) = sqrt(a)/sqrt(b) ---- ---- v 1 v -1 ***************************************************************************** ---- ---- ---- ---- 5. v -1 * v -1 = v 1 * v 1 cross multiply ***************************************************************************** 6. -1 = 1 Q.E.D. (?!? Surprise ?!?) ***************************************************************************** ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.