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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
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