A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The most common example of
a mathematical fallacy is the ``proof'' that as follows. Let , then

The incorrect step is division by (equal to 0), which is invalid. Ball and Coxeter (1987) give other such examples in the areas of both arithmetic and geometry.

**References**

Ball, W. W. R. and Coxeter, H. S. M. *Mathematical Recreations and Essays, 13th ed.*
New York: Dover, pp. 41-45 and 76-84, 1987.

Pappas, T. ``Geometric Fallacy & the Fibonacci Sequence.'' *The Joy of Mathematics.*
San Carlos, CA: Wide World Publ./Tetra, p. 191, 1989.

© 1996-9

1999-05-26