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Index of Subjects Hi Dave ( a - b - c) = 0; What he says is nothing equals nothing! Sound good to me. Many a computer programmer spent long hours figuring that one out - been there - done that! Have a nice winter Paul --- David & Alison Webster <dwebster@glinx.com> wrote: > Dear All, Dec 20, 2006 > I recently came across an old article about > Raymond Smullyan, a > highschool dropout who e.g. satisfied the course > requirements for a PhD > in Math and Philosophy by teaching the required > courses. He also created > many logic puzzles. One thing leads to another, so I > blew the dust off > of an old copy of Martin Gardner's 1959 Mathematical > Puzzles and > Diversions. > > One of his fallacies follows. I hope you have > not seen this previously. > Proof that unequal numbers are equal > > Given two numbers a & b such that b is smaller > than a by an amount > c; thus > > a = b + c > > prove that a = b > > multiply both sides by (a - b) to obtain-- > > a^2 - ab = ab +ac - b^2 - bc > > subtract ac from both sides to obtain > > a^2 - ab - ac = ab - b^2 - bc > > Factor : > a ( a - b -c) = b ( a - b -c) > > Divide both sides by ( a - b - c) to obtain > > a = b > > QED > > "The road to correct conclusions is full of > pitfalls" (DHW, Dec 20, > 2006). > > Merry Christmas, Dave Webster, Kentville > > > > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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